2017
8
2
0
137
Autobiography of Roberto Todeschini
2
2
1

93
105


R.
Todeschini
Milano Chemometrics and QSAR Research Group
Milano Chemometrics and QSAR Research Group
Italy
roberto.todeschini@unimib.it
[Ballabio, D., Biganzoli, F., Todeschini, R. and Consonni, V. (2016) Qualitative consensus of QSAR ready biodegradability predictions. Toxicological and Environmental Chemistry, in press.##Cassotti, M., Grisoni, F., Nembri, S. and Todeschini, R. (2016) Application of the weighted PowerWeakness Ratio (wPWR) as a fusion rule in ligandbased virtual screening. MATCH Commun. Math. Comput. Chem., 76, 359–376.##Grisoni, F., Consonni, V., Vighi, M., Villa, S. and Todeschini, R. (2016) Investigating the mechanisms of bioconcentration through QSAR classification trees. Environmental International, 88, 198–205.##Grisoni, F., Consonni, V., Vighi, M., Villa, S. and Todeschini, R. (2016) Expert QSAR system for predicting the bioconcentration factor under the REACH regulation. EnvironmentalResearch, 148, 507–512.##Grisoni, F., Reker, D., Schneider, P., Friedrich, L., Consonni, V., Todeschini, R., Koberle, A., Werz, O. and Schneider, G. (2016) Matrixbased molecular descriptors for prospective virtual compound screening. MolecularInformatics, 35.##Mauri, A., Consonni, V. and Todeschini, R. (2016) Molecular Descriptors, in Handbook of Computational Chemistry (ed. T. Puzyn), Springer.##Mauri, A., Ballabio, D., Todeschini, R. and Consonni, V. (2016) Mixtures, metabolites, ionic liquids: anew measure to evaluate similarity between complex chemical systems. Journal of Cheminformatics, 8, 13.##Nembri, S., Grisoni, F., Consonni, V. and Todeschini, R. (2016) In silico prediction of Cytochrome P450  Drug interaction: QSARs for CYP3A4 and CYP2C9. International Journal of MolecularSciences, 17, 1–19.##Rojas, Ch., Ballabio, D., Consonni, V., Tripaldi, P., Mauri, A. and Todeschini, R. (2016) Quantitative StructureActivity Relationships to predict sweet and nonsweet tastes. TheoreticalChemistry Accounts, 135–166.##Todeschini, R., Ballabio, D., Grisoni, F. and Consonni, V. (2016) A new concept of secondorder similarity and the role od distance/similarity measures in local classification methods. Chemometrics &Intell. Lab. Syst., 157, 50–57.##Todeschini, R. and Baccini, A. (2016) Handbook of Bibliometric Indicators, WileyVCH, Weinheim (Germany), 512 pp.##Todeschini, R., Ballabio, D. and Grisoni, F. (2016) Beware of unreliable Q2! A comparative study of regression metrics for predictivity assessment of QSAR models. Journal of Chemical Information and Modeling, 56, 19051913.##Cassotti, M., Ballabio, D., Todeschini, R. and Consonni, V. (2015) A similaritybased QSAR model for predicting acute toxicity towards the fathead minnow (Pimephalespromelas). SAR & QSAR in EnvironmentalResearch, 26, 217–243.##Grisoni, F., Consonni, V., Nembri, S. and Todeschini, R. (2015) How to weight Hasse matrices and reduce incomparabilities. Chemometrics &Intell. Lab. Syst., 147, 95–104.##Grisoni, F., Consonni, V., Villa, S., Vighi, M. and Todeschini, R. (2015) QSAR models for bioconcentration: is the increase in the complexity justified by more accurate predictions? Chemosphere, 127, 171–179.##Mansouri, K. and et al. (2015) CERAPP: Collaborative Estrogen Receptor Activity Prediction Project. EnvironmentalHealthPerspectives, 124, 1023–1033.##Todeschini, R., Ballabio, D. and Consonni, V. (2015) Distances and Other Dissimilarity Measures in Chemometrics, inEncyclopedia of Analytical Chemistry Wiley & Sons, pp. 1–60.##Todeschini, R., Nembri, S. and Grisoni, F. (2015) Weighted PowerWeakness Ratio for multicriteria decision making. Chemometrics &Intell. Lab. Syst., 146, 329–336.##Todeschini, R., Ballabio, D., Cassotti, M. and Consonni, V. (2015) N3 and BNN: Two new similarity based classification methods in comparison with other classifiers. Journal of Chemical Information and Modeling, 55, 2365–2375.##Ballabio, D., Consonni, V., Mauri, A., ClaeysBruno, M., Sergent, M. and Todeschini, R. (2014) A novel variable reduction method adapted from spacefilling designs. Chemometrics &Intell. Lab. Syst., 136, 147–154.##Buscema, M., Consonni, V., Ballabio, D., Mauri, A., Massini, G., Breda, M. and Todeschini, R. (2014) KCM: a new artificialneural network. Application to supervised pattern recognition. Chemometrics &Intell. Lab. Syst., 138, 110–119.##Cassotti, M., Ballabio, D., Consonni, V., Mauri, A., Tetko, I.V. and Todeschini, R. (2014) Prediction of acute aquatic toxicity toward daphnia magna using GAkNN methods. ATLA, 42, 31–41.##Cassotti, M., Grisoni, F. and Todeschini, R. (2014) Reshaped Sequential Replacement algorithm: an efficient approach to variable selection. Chemometrics &Intell. Lab. Syst., 133, 136–148.##Cherkasov, A., Muratov, E., Fourches, D., Varnek, A., Baskin, I., Cronin, M.T.D., Dearden, J., Gramatica, P., Martin, Y.C., Todeschini, R., Consonni, V., Kuz'min, V., Cramer, R., Benigni, R., Yang, C., Richrad, A., Terfloth, L., Gasteiger, J. and Tropsha, A. (2014) QSAR Modeling: Where have you been? Where are yougoing to? Journal MedicinalChemistry, 57, 4997–5010.##Grisoni, F., Cassotti, M. and Todeschini, R. (2014) Reshaped Sequential Replacement algorithm for variable selection in QSPR modelling: comparison with other benchmark methods. Journal of Chemometrics, 28, 249–259.##Sahigara, F., Ballabio, D., Todeschini, R. and Consonni, V. (2014) Assessing the validity of QSARs for ready biodegradability of chemicals: An Applicability Domain perspective. Current ComputerAidedDrug Design, 10, 137–147.##Swapnil, C., Nicholls, I., Karlsson, B., Rosengren, A., Ballabio, D., Consonni, V. and Todeschini, R. (2014) Towards Global QSAR Model Building for Acute Toxicity: Munro Database Case Study. International Journal of MolecularSciences, 15, 18162–18174.##Tetko, I.V., Schramm, K.W., Knepper, T., Peijnenburg, W.J.G.M., Hendriks, A.J., Nicholls, I.A., Öberg, T., Todeschini, R., Schlosser, E. and Brandmaier, S. (2014) The Experimental and Theoretical Studies within the FP7 Environmental ChemOinformatics Marie Curie Initial Training Network 'ECO'. ATLA, 42, 1–5.##Todeschini, R., Consonni, V., Ballabio, D., Mauri, A., Cassotti, M., Lee, S., West, A. and Cartlidge, D. (2014) QSPR study of rheological and mechanical properties of Chloroprene rubber accelerators. RubberChemistry and Technology, 87, 219–238.##Mansouri, K., Ringsted, T., Ballabio, D., Todeschini, R. and Consonni, V. (2013) Quantitative StructureActivity Relationship models for ready biodegradability of chemicals. Journal of Chemical Information and Modeling, 53, 867–878.##Sahigara, F., Ballabio, D., Todeschini, R. and Consonni, V. (2013) Defining a novel kNearest Neighbours approach to assess the applicability of a QSAR model for reliable predictions. Journal of Chemoinformatics, 5, 1–9.##Todeschini, R., Ballabio, D., Consonni, V., Sahigara, F. and Filzmoser, P. (2013) Locallycentred Mahalanobis distance: a new distance measure with salient features towards outlier detection. Anal. Chim. Acta, 787, 1–9.##Consonni, V. and Todeschini, R. (2012) Multivariate Analysis of Molecular Descriptors, in Statistical Modelling of Molecular Descriptors in QSAR/QSPR (eds. M. Dehmer, K. Varmuza and D. Bonchev), WileyBlackwell, Weinheim (Germany), pp. 111–147.##Consonni, V. and Todeschini, R. (2012) New similarity coefficients for binary data. MATCH Commun. Math. Comput. Chem., 68, 581–592.##Ippolito, A., Todeschini, R. and Vighi, M. (2012) Sensitivity assessment of freshwater macroinvertebrates to pesticides using biological traits. Ecotoxicology, 21, 336–352.##Mansouri, K., Consonni, V., Durjava, M.K., Kolar, B., Öberg, T. and Todeschini, R. (2012) Assessing bioaccumulation of polybrominated diphenyl ethers for aquatic species by QSAR modeling. Chemosphere, 89, 433–444.##Nielsen, N.J., Ballabio, D., Tomasi, G., Todeschini, R. and Christensen, J.H. (2012) Chemometric analysis of GCFID chromatograms (CHEMFID): A novel method for classification of petroleum products. J. Chromat. A, 1238, 121–127.##Sahigara, F., Mansouri, K., Ballabio, D., Mauri, A., Consonni, V. and Todeschini, R. (2012) Comparison of Different Approaches to Define the Applicability Domain of QSAR Models. Molecules, 17, 4791–4810.##Todeschini, R., Consonni, V., Xiang, H., Holliday, J., Buscema, M. and Willett, P. (2012) Similarity coefficients for binary chemoinformatics data: overview and extended comparison using simulated and real datasets. Journal of Chemical Information and Modeling, 52, 2884–2901.##Consonni, V. and Todeschini, R. (2011) Structure  Activity Relationships by autocorrelation descriptors and genetic algorithms, inChemoinformatics and Advanced Machine Learning Perspectives: Complex Computational Methods and Collaborative Techniques (eds. H. Lohdi and Y. Yamanishi), IGI Global Publishers, Hershey, PA (USA), pp. 60–93.##Sushko, I., Novotarskyi, S., Körner, R., Pandey, A.K., Rupp, M., Teetz, W., Brandmaier, S., Abdelaziz, A., Prokopenko, V.V., Tanchuk, V.Y., Todeschini, R., Varnek, A., Marcou, G., Ertl, P., Potemkin, V., Grishina, M., Gasteiger, J., Schwab, C., Baskin, I., Palyulin, V.A., Radchenko, E.V., Welsh, W.J., Kholodovych, V., Chekmarev, D., Cherkasov, A., AiresdeSousa, J., Zhang, Q.Y., Bender, A., Nigsch, F., Patiny, L., Williams, A., Tkachenko, V. and Tetko, I.V. (2011) Online chemical modeling environment (OCHEM): web platform for data storage, model development and publishing of chemical information. J. ComputerAidedMol. Des., 25, 533–554.##Todeschini, R. (2011) The jindex: a new bibliometric index and multivariate comparisons between other common indices. Scientometrics, 87, 621–639.##Ballabio, D., Consonni, V., Mauri, A. and Todeschini, R. (2010) Canonical Measure of Correlation (CMC) and Canonical Measure of Distance (CMD) between sets of data. Part 3. Variableselection in classification. Anal. Chim. Acta, 657, 116–122.##Ballabio, D. and Todeschini, R. (2010) Geographical characterization of olive oil by means of multivariate classification: application of CAIMAN, in Olives and olive oil in health and disease prevention (eds. V. R. Preedy and R. R. Watson), Elsevier, Amsterdam, pp. 131–139.##Consonni, V. and Todeschini, R. (2010) Molecular Descriptors, in Recent Advances in QSAR Studies: Methods and Applications, Vol. 8 (eds. M. T. D. Cronin, J. Leszczynski and T. Puzyn), Springer, Amsterdam (The Netherlands), pp. 29–102.##Consonni, V., Ballabio, D. and Todeschini, R. (2010) Evaluation of model predictive ability by external validation techniques. Journal of Chemometrics, 24, 194–201.##Consonni, V., Ballabio, D. and Todeschini, R. (2010) Enhancing Chemical Information in QSAR: Generalized GraphTheoretical Matrices, in Novel Molecular Structure Descriptors  Theory and Applications II (eds. I. Gutman and B. Furtula), University of Kragujevac, Kragujevac (Serbia), pp. 21–55.##FernandezVarela, R., GomezCarracedo, M.P., Ballabio, D., Andrade, J.M., Consonni, V. and Todeschini, R. (2010) Self Organizing Maps For Analysis Of Polycyclic Aromatic Hydrocarbons 3Way Data From Spilled Oils. AnalyticalChemistry, 82, 4264–4271.##Sushko, I., Novotarskyi, S., Körner, R., Pandey, A.K., Cherkasov, A., Li, J., Gramatica, P., Hansen, K., Schroeter, T., Müller, K.R., Xi, L., Liu, H., Yao, X., Öberg, T., Hormozdiari, F., Dao, P., Sahinalp, C., Todeschini, R., Polishchuk, P., Artemenko, A., Kuz'min, V., Martin, T.M., Young, D.M., Fourches, D., Muratov, E., Tropsha, A., Baskin, I., Horbath, D., Marcou, G., Varnek, A., Prokopenko, V.V. and Tetko, I.V. (2010) ApplicabilityDomains for ClassificationProblems: Benchmarking of Distance to Models for AmesMutagenicity Set. Journal of Chemical Information and Modeling, 50, 2094–2111.##Todeschini, R. and Consonni, V. (2010) New local vertex invariants and molecular descriptors based on functions of the vertex degrees. MATCH Commun. Math. Comput. Chem., 64, 359–372.##Todeschini, R., Ballabio, D. and Consonni, V. (2010) Novel Molecular Descriptors Based on Functions of New Vertex Degrees, in Novel Molecular Structure Descriptors  Theory and Applications I (eds. I. Gutman and B. Furtula), University of Kragujevac, Kragujevac (Serbia), pp. 73–100.##Ballabio, D. and Todeschini, R. (2009) Multivariate Classification for Qualitative Analysis, in Infrared Spectroscopy for Food Quality Analysis and Control (ed. S. DaWen), Elsevier, Amsterdam, pp. 83–104.##Ballabio, D., Manganaro, A., Consonni, V., Mauri, A. and Todeschini, R. (2009) Introduction to MOLE DB – online MolecularDescriptors Database. MATCH Commun. Math. Comput. Chem., 62, 199–207.##Ballabio, D., Consonni, V. and Todeschini, R. (2009) The Kohonen and CPANN toolbox: a collection of MATLAB modules for Self Organising Maps and Counterpropagation Artificial Neural Networks. Chemometrics &Intell. Lab. Syst., 98, 115–122.##Consonni, V., Ballabio, D., Manganaro, A., Mauri, A. and Todeschini, R. (2009) Canonical Measure of Correlation (CMC) and Canonical Measure of Distance (CMD) between sets of data. Part 2. Variablereduction. Anal. Chim. Acta, 648, 52–59.##Consonni, V., Ballabio, D. and Todeschini, R. (2009) Comments on the definition of the Q2 parameter for QSAR validation. Journal of Chemical Information and Modeling, 49, 1669–1678.##Pavan, M. and Todeschini, R. (2009) Multicriteria Decision Making Methods, in Comprehensive Chemometrics, Vol. 1 (eds. B. Walczak, R. Taulér and S. Brown), Elsevier, Amsterdam (The Netherlands), pp. 591–629.##Piazza, L., Gigli, J., Rojas, Ch., Ballabio, D., Todeschini, R. and Tripaldi, P. (2009) Dairy Cream Response In Instrumental Texture Evaluation Processed By Multivariate Analysis. Chemometrics &Intell. Lab. Syst., 96, 258–263.##Todeschini, R., Consonni, V. and Gramatica, P. (2009) Chemometrics in QSAR, in Comprehensive Chemometrics, vol. 4, Vol. 4 (eds. S. Brown, B. Walczak and R. Taulér), Elsevier, Oxford (UK), pp. 129–172.##Todeschini, R. and Consonni, V. (2009) Molecular Descriptors for Chemoinformatics (2 volumes), Vol. 41, WILEYVCH, Weinheim (Germany), 1257 pp.##Todeschini, R., Consonni, V., Manganaro, A., Ballabio, D. and Mauri, A. (2009) Canonical Measure of Correlation (CMC) and Canonical Measure of Distance (CMD) between sets of data. Part 1. Theory and simple chemometric applications. Anal. Chim. Acta, 648, 45–51.##Consonni, V. and Todeschini, R. (2008) New Spectral Indices for Molecule Description. MATCH Commun. Math. Comput. Chem., 60, 3–14.##Gutman, I., Indulal, G. and Todeschini, R. (2008) Generalizing the McClelland Bounds for Total Electron Energy. ZeitschriftfürNaturforschung A, 63a, 280–282.##Manganaro, A., Ballabio, D., Consonni, V., Mauri, A., Pavan, M. and Todeschini, R. (2008) The DART (Decision Analysis by Ranking Techniques) software, in Scientific Data Ranking Methods: Theory and Applications (eds. M. Pavan and R. Todeschini), Elsevier, Amsterdam (The Netherlands), pp. 193–207.##Mauri, A., Ballabio, D., Consonni, V., Manganaro, A. and Todeschini, R. (2008) Peptides multivariate characterisation using a molecular descriptor based approach. MATCH Commun. Math. Comput. Chem., 60, 671–690.##Pavan, M. and Todeschini, R. (2008) Total order ranking methods, in Scientific Data Ranking Methods: Theory and Applications(eds. M. Pavan and R. Todeschini), Elsevier, Amsterdam (The Netherlands), pp. 51–72.##Todeschini, R. and Pavan, M., Eds. (2008) Scientific Data Ranking Methods: Theory and Applications.Elsevier, Amsterdam (The Netherlands), 180 pp.##Tetko, I.V., Sushko, I., Pandey, A.K., Zhu, H., Tropsha, A., Papa, E., Õberg, T., Todeschini, R., Fourches, D. and Varnek, A. (2008) Critical assessment of QSAR models of environmental toxicity against Tetrahymena pyriformis: Focusing on applicability domain and overfitting by variable selection. Journal of Chemical Information and Modeling, 48, 1733–1746.##Todeschini, R., Ballabio, D., Consonni, V. and Mauri, A. (2008) A new similarity/diversity measure for the characterization of DNA sequences. CroaticaChemica Acta, 81, 657–664.##Ballabio, D., Consonni, V. and Todeschini, R. (2007) Classification of multiway analytical data based on MOLMAP approach. Anal. Chim. Acta, 605, 134–146.##Ballabio, D., Kokkinofta, R., Todeschini, R. and Theocharis, C.R. (2007) A classification model built by means of Artificial Neural Networks for the characterization of the traditional Cypriot spirit Zivania. Chemometrics &Intell. Lab. Syst., 87, 78–84.##Todeschini, R., Ballabio, D., Consonni, V., Mauri, A. and Pavan, M. (2007) CAIMAN (Classification And Influence Matrix Analysis): A new approach to the classification based on leveragescaled functions. Chemometrics &Intell. Lab. Syst., 87, 3–17.##Todeschini, R., Ballabio, D., Consonni, V. and Mauri, A. (2007) A new similarity/diversity measure for sequential data. MATCH Commun. Math. Comput. Chem., 57, 51–67.##Ballabio, D., Mauri, A., Todeschini, R. and Buratti, S. (2006) Geographical classification of wine and olive oil by means of CAIMAN (Classification And Influence Matrix Analysis). Anal. Chim. Acta, 570, 249–258.##Ballabio, D., Cosio, M.S., Mannino, S. and Todeschini, R. (2006) A chemometric approach based on a novel similarity/diversity measure for the characterization and selection of electronic nose sensors. Anal. Chim. Acta, 578, 170–177.##Mauri, A., Consonni, V., Pavan, M. and Todeschini, R. (2006) DRAGON software: an easy approach to molecular descriptor calculations. MATCH Commun. Math. Comput. Chem., 56, 237–248.##Pavan, M., Consonni, V., Gramatica, P. and Todeschini, R. (2006) New QSAR modelling approach based on ranking models by Genetic Algorithms  Variable Subset Selection (GAVSS), in Partial Order in Environmental Sciences and Chemistry (eds. R. Brüggeman and L. Carlsen), SpringerVerlag, pp. 185–224.##Todeschini, R. (2006) Molecular Descriptors and Chemometrics. G. I. T. Laboratory Journal, 5, 40–42.##Todeschini, R., Consonni, V., Mauri, A. and Ballabio, D. (2006) Characterization of DNA primary sequences by a new similarity/diversity measure based on the partial ordering. Journal of Chemical Information and Modeling, 46, 1905–1911.##Pavan, M., Consonni, V. and Todeschini, R. (2005) Partial Ranking Models by Genetic Algorithms Variable Subset Selection (GAVSS) approach for environmental priority settings. MATCH Commun. Math. Comput. Chem., 54, 583–609.##Tetko, I.V., Gasteiger, J., Todeschini, R., Mauri, A., Livingstone, D., Ertl, P., Palyulin, V.A., Radchenko, E.V., Zefirov, N.S., Makarenko, A.S., Tanchuk, V.Y. and Prokopenkov, V.V. (2005) Virtual ComputationalChemistryLaboratory  Design and Description. J. ComputerAidedMol. Des., 19, 453–463.##Pavan, M. and Todeschini, R. (2004) New indices for analyzing partial ranking diagrams. Anal. Chim. Acta, 515, 167–181.##Pavan, M., Mauri, A. and Todeschini, R. (2004) Total ranking models by the Genetic Algorithms Variable Subset Selection (GAVSS) approach for environmental priority settings. Analytical and BioanalyticalChemistry, 380, 430–444.##Todeschini, R., Consonni, V., Mauri, A. and Pavan, M. (2004) New fitness functions to avoid bad regression models in variable subset selection by Genetic Algorithms, (eds. M. Ford, D. Livingstone, J. Deardean and H. van de Waterbeemd), Blakwell, Oxford (UK), pp. 323–325.##Todeschini, R., Consonni, V., Mauri, A. and Pavan, M. (2004) Detecting "bad" regression models: multicriteria fitness functions in regression analysis. Anal. Chim. Acta, 515, 199–208.##Todeschini, R., Consonni, V. and Pavan, M. (2004) A Distance Measure between Models: a Tool for Similarity/Diversity Analsysis of Model Populations. Chemometrics &Intell. Lab. Syst., 70, 55–61.##Backhaus, T., Altenburger, R., Arrhenius, A., Blanck, H., Faust, M., Finizio, A., Gramatica, P., Grothe, M., Junghans, M., Meyer, W., Pavan, M., Porspring, T., Scholze, M., Todeschini, R., Vighi, M., Walter, H. and Grimme, L.H. (2003) The BEAMproject: prediction and assessment of mixture toxicities in the aquatic environment. Continental ShelfResearch, 23, 1757–1769.##Lleti, R., Sarabia, L., Ortiz, M.C., Todeschini, R. and Colombini, M.P. (2003) Application of the Kohonen Artificial Neural Network in the identification of Proteinaceous Binders in Samples of Panel Painting Using Gas ChromatographyMass Spectrometry. The Analyst, 181, 281–286.##Mezzanotte, V., Castiglioni, F., Todeschini, R. and Pavan, M. (2003) Study on anaerobic and aerobic degradation of different nonionic surfactants. Bioresource Technology, 87, 87–91.##Todeschini, R., Consonni, V. and Pavan, M. (2003) MobyDigs: Software for Regression and Classification Models by Genetic Algorithms, in Natureinspired Methods in Chemometrics: Genetic Algorithms and Artificial Neural Networks (ed. R. Leardi), Elsevier, Amsterdam (The Netherlands), pp. 141–167.##Todeschini, R. and Consonni, V. (2003) Descriptors from Molecular Geometry, in Handbook of Chemoinformatics  Vol.3, Vol. 3 (ed. J. Gasteiger), WILEYVCH, Weinheim (GER), pp. 1004–1033.##Todeschini, R., Consonni, V. and Pavan, M. (2003) Distance measure between models: a tool for model similarity/diversity analysis, in Designing Drugs and Crop Protectants: processes, problems and solutions. (eds. M. Ford, D. Livingstone, J. Deardean and H. van de Waterbeemd), Blakwell, Oxford (UK), pp. 467–469.##Consonni, V., Todeschini, R. and Pavan, M. (2002) Structure/Response Correlations and Similarity/Diversity Analysis by GETAWAY Descriptors. 1. Theory of the Novel 3D Molecular Descriptors. Journal of Chemical Information and Computer Sciences, 42, 682–692.##Consonni, V., Todeschini, R., Pavan, M. and Gramatica, P. (2002) Structure/Response Correlations and Similarity/Diversity Analysis by GETAWAY Descriptors. 2. Application of the Novel 3D Molecular Descriptors to QSAR/QSPR Studies. Journal of Chemical Information and Computer Sciences, 42, 693–705.##Benicori, T., Consonni, V., Gramatica, P., Pilati, T., Rizzo, S., Sannicolò, F., Todeschini, R. and Zotti, G. (2001) Steric Control of Conductivity in Highly ConjugatedPolythiophenes. Chemistry of Materials, 13, 1665–1673.##Di Marzio, W., Galassi, S., Todeschini, R. and Consolaro, F. (2001) Traditional versus WHIM molecular descriptors in QSAR approaches applied to fish toxicity studies. Chemosphere, 44, 401–406.##Gramatica, P., Vighi, M., Consolaro, F., Todeschini, R., Finizio, A. and Faust, M. (2001) QSAR approach for the selection of congeneric compounds with a similar toxicological mode of action. Chemosphere, 42, 873–883.##Vighi, M., Gramatica, P., Consolaro, F. and Todeschini, R. (2001) QSAR and Chemometric Approaches for Setting Water Quality Objectives for Dangerous Chemicals. Ecotoxicology and EnvironmentalSafety, 49, 206–220.##CapitanVallvey, L.F., Navas, N., del Olmo, M., Consonni, V. and Todeschini, R. (2000) Resolution of mixtures of three nonsteroidal antiinflammatory drugs by fluorescence using partial least squares multivariate calibration with previous wavelength selection by Kohonen artificial neural networks. Talanta, 52, 1069–1079.##Todeschini, R. and Consonni, V. (2000) Handbook of Molecular Descriptors, WileyVCH, Weinheim (Germany), 668 pp.##]
A novel topological descriptor based on the expanded wiener index: Applications to QSPR/QSAR studies
2
2
In this paper, a novel topological index, named Mindex, is introduced based on expanded form of the Wiener matrix. For constructing this index the atomic characteristics and the interaction of the vertices in a molecule are taken into account. The usefulness of the Mindex is demonstrated by several QSPR/QSAR models for different physicochemical properties and biological activities of a large number of diversified compounds. Moreover, the applicability of the proposed index has been checked among isomeric compounds. In each case the stability of the obtained model is confirmed by the cross validation test. The results of present study indicate that the Mindex provides a promising route for developing highly correlated QSPR/QSAR models. On the other hand, the Mindex is easy to generate and the developed QSPR/QSAR models based on this index are linearly correlated. This is an interesting feature of the Mindex when compared with quantum chemical descriptors which require vast computational cost and exhibit limitations for large sized molecules.
1

107
135


A.
Mohajeri
Shiraz University
Shiraz University
Iran
mohajeriaf@gmail.com


P.
Manshour
Persian Gulf University
Persian Gulf University
Iran


M.
Mousaee
Shiraz University
Shiraz University
Iran
mahboub.mousaee@gmail.com
topological index
Graph theory
Expanded Wiener index
QSPR
QSAR
[A.L. Barabási, Linked: The New Science of Networks, Perseus Publishing, Cambridge, 2003.##A.T. Balaban, Chemical Applications of Graph Theory, Academic Press, London, 1976.##A.T. Balaban, From chemical graphs to 3D molecular modeling, in: A. T. Balaban (Ed.), From Chemical Topology to Three–Dimensional Geometry, Plenum Press, New York, 1997, pp. 1–24.##L. Euler, Solutio problematisadgeometriam situs pertinentis, Commentarii Academiae Scientiarum Petropolitanae 8 (1741) 128–140.##N. Trinajstić, Chemical Graph Theory, CRC Press, Florida, USA, 1992.##Q. Ivanciuc, QSAR comparative study of Wiener descriptors for weighted molecular graphs, J. Chem. Inf. Comput. Sci. 40 (2000) 1412–1422.##A. Mohajeri, M. Alipour, M. B. Ahmadi, A graph theory study on (ZnS)n (n= 3–10) nanoclusters, Chem. Phys. Lett. 503 (2011) 162–166.##A. Kurup, R. Garg, C. Hansch, Comparative QSAR study of tyrosine kinase inhibitors, Chem. Rev. 101 (2001) 2573–2600.##R. García–Domenech, J. Gálvez, J. V. de Julián–Ortiz, L. Pogliani, Some new trends in chemical graph theory, Chem. Rev.108 (2008) 1127–1169.##C. Cao, Y. Hua, Topological indices based on vertex, distance, and ring: On the boiling points of paraffins and cycloakanes, J. Chem. Inf. Comput. Sci. 41 (2001) 867–877.##H. Yuan, A. L. Parrill, QSAR development to describe HIV–1 integrase inhibition, J. Mol. Struct. (THEOCHEM) 529 (2000) 273–282.##A. Mohajeri, M. H. Dinpajooh, Structure–toxicity relationship for aliphatic compounds using quantum topological descriptors, J. Mol. Struct. (THEOCHEM) 855 (2008) 1–5.##B. Hemmateenejad, A. Mohajeri, Application of quantum topological molecular similarity descriptors in QSPR study of the O–methylation of substituted phenols, J. Comput. Chem. 29 (2008) 266–274.##R. Todeschini, V. Consonni, Handbook of Molecular Descriptors, Wiley VCH, Weinheim, 2000.##H. Wiener, Structural determination of paraffin boiling points, J. Am. Chem. Soc. 69 (1947) 17–20.##A. T. Balaban, Highly discriminating distance–based topological index, Chem. Phys. Lett. 89 (1982) 399–404.##M. Randić, Characterization of molecular branching, J. Am. Chem. Soc. 97 (1975) 6609–6615.##H. Hosoya, Topological index. A newly proposed quantity characterizing the topological nature of structural isomers of saturated hydrocarbons, Bull. Chem. Soc. Jpn. 44 (1971) 2332–2339.##D. H. Rouvray, The role of the topological distance matrix in chemistry, in: N. Trinajstić (Ed.), Mathematics and Computational Concepts in Chemistry, Horwood, Chichester, 1986, pp. 295–306.##I. Gutman, J. H. Potgieter, Wiener index and intermolecular forces, J. Serb. Chem. Soc. 62 (1997) 185–192.##D. H. Rouvray, Should we have designs on topological indices? Chemical Applications of Topology and Graph Theory, Stud. in Phys. & Theoret. Chem., Elsevier, Amsterdam, 1983, pp. 159–177.##I. Lukovits, Wiener–type graph invariants, in: M. V. Diudea (Ed.), QSPR/QSAR Studies by Molecular Descriptors, Nova Science, Huntington, 2001, pp. 31–38.##I. Gutman, J. Žerovnik, Corroborating a modification of the Wiener index, Croat. Chem. Acta. 75 (2002) 603–612.##O. Ivanciuc, T. Ivanciuc, A. T. Balaban, Design of topological indices, part 10.1: Parameters based on electronegativity and covalent radius for the computation of molecular graph descriptors for heteroatom–containing molecules, J. Chem. Inf. Comput. Sci. 38 (1998) 395–401.##F. Yang, Z. D. Wang, Y. P. Huang, X. R. Ding, Modification of Wiener index and its application, J. Chem. Inf. Comput. Sci. 43 (2003) 753–756.##F. Yang, Z. D. Wang, Y. P. Huang, P. J. Zhou, Modification of the Wiener index 2, J. Chem. Inf. Comput. Sci. 43 (2003) 1337–1341.##F. Yang, Z. D. Wang, Y. P. Huang, H. L. Zhu, Novel topological index F based on incidence matrix, J. Comput. Chem. 24 (2003) 1812–1820.##F. Yang, Z. D. Wang, Y. P. Huang, Modification of the Wiener index 4, J. Comput. Chem. 25 (2004) 881–887.##S. S. Tratch, M. I. Stankevitch, N. S. Zefirov, Combinatorial models and algorithms in chemistry. The expanded Wiener number–A novel topological index, J. Comput. Chem. 11 (1990) 899–908.##P. V. Khadikar, S. Karmarkar, A novel PI index and its applications to QSPR/QSAR studies, J. Chem. Inf. Comput. Sci. 41 (2001) 934–949.##R. Walsh, Thermochemistry of Silicon–containing compounds, J. Chem. Soc. Faraday Trans. 79 (1983) 2233–2248.##X. Zhihong, W. Leshan, The Data Base of Inorganic Chemical Thermodynamics, Science Press, Beijing, 1987.##J. G. Stark, H. G. Wallace, Chemistry Data Book, John Murray, London, 1982.##G. Gini, M. V. Craciun, C. König, Combining unsupervised and supervised artificial neural networks to predict aquatic toxicity, J. Chem. Inf. Comp. Sci. 44 (2004) 1897–1902.##Y. Xue, H. Li, C. Y. Ung, C. W. Yap, Y. Z. Chen, Classification of a diverse set of Tetrahymena pyriformistoxicity chemical compounds from molecular descriptors by statistical learning methods, Chem. Res. Toxicol. 19 (2006) 1030–1039.##T. W. Schultz, Tetratox: Tetrahymena pyriformis population growth impairment endpoint a surrogate for fish lethality, Toxicol. Mech. Method 7 (1997) 289–309.##D. R. Roy, R. Parthasarathi, B. Maiti, V. Subramanian, P. K. Chattaraj, Electrophilicity as a possible descriptor for toxicity prediction, Bioorg. Med. Chem. 13 (2005) 3405–3412.##C. L. Yaws, Chemical Properties Handbook, McGraw–Hill, New York, 1999.##E. Estrada, L. Rodriguez, A. Gutiétrez, Matrix algebraic manipulations of molecular graphs. 1. Distance and Vertex–Adjacency Matrices, MATCH Commun. Math. Comput. Chem. 35 (1997) 145–156.##R. C. Weast, CRC Handbook of Chemistry and Physics, CRC Press, Boca Raton, FL, 1989.##D. R. Lide, G. W. A. Milne, Handbook of Data on Common Organic Compounds, CRC Press, Boca Raton, FL, 1995.##J. A. Dean, Lange’s Handbook of Chemistry, McGraw–Hill, New York, 1999.##A. A. Gakh, E. G. Gakh, B. G. Sumpter, D. W. Noid, Neural network–graph theory approach to the prediction of the physical properties of organic compounds, J. Chem. Inf. Comput. Sci. 34 (1994) 832–839.##]
A new twostep Obrechkoff method with vanished phaselag and some of its derivatives for the numerical solution of radial Schrodinger equation and related IVPs with oscillating solutions
2
2
A new twostep implicit linear Obrechkoff twelfth algebraic order method with vanished phaselag and its first, second, third and fourth derivatives is constructed in this paper. The purpose of this paper is to develop an efficient algorithm for the approximate solution of the onedimensional radial Schrodinger equation and related problems. This algorithm belongs in the category of the multistep methods. In order to produce an efficient multistep method the phaselag property and its derivatives are used. An error analysis and a stability analysis is also investigated and a comparison with other methods is also studied. The efficiency of the new methodology is proved via theoretical analysis and numerical applications.
1

137
159


A.
Shokri
Department of Mathematics, Faculty of Basic Science, University of Maragheh, Maragheh, Iran.
Department of Mathematics, Faculty of Basic
Iran
shokri2090@gmail.com


M.
Tahmourasi
Department of Mathematics, Faculty of Basic Science, University of Maragheh, Maragheh, Iran.
Department of Mathematics, Faculty of Basic
Iran
mortazatahmoras@gmail.com
Schrodinger equation
Phaselag
Ordinary differential equations
Symmetric multistep methods
[[1] U. Ananthakrishnaiah, P–stable Obrechkoff methods with minimal phase–lag for periodic initial value problems, Math. Comput. 49 (1987) 553–559.##[2] M. Asadzadeh, D. Rostamy and F. Zabihi, Discontinuous Galerkin and multiscale variational schemes for a coupled damped nonlinear system of Schrödinger equations, J. Numer. Methods Partial Differential Equations 29 (6) (2013) 1912–1945.##[3] M. M. Chawla, P. S. Rao, A Numerov–type method with minimal phase–lag for the integration of second order periodic initial value problems. II: Explicit method, J. Comput. Appl. Math. 15 (1986) 329–337.##[4] M. M. Chawla, P. S. Rao, An explicit sixth–order method with phase–lag of order eight for , J. Comput. Appl. Math. 17 (1987) 363–368.##[5] G. Dahlquist, On accuracy and unconditional stability of linear multistep methods for second order differential equations, BIT 18 (1978) 133–136.##[6] J. M. Franco, An explicit hybrid method of Numerov type for second–order periodic initial–value problems, J. Comput. Appl. Math. 59 (1995) 79–90.##[7] J. M. Franco, M. Palacios, High–order P–stable multistep methods, J. Comput. Appl. Math. 30 (1990) 1–10.##[8] W. Gautschi, Numerical integration of ordinary differential equations based on trigonometric polynomials, Numer. Math. 3 (1961) 381–397.##[9] A. Ibraheem, T. E. Simos, A family of high–order multistep methods with vanished phase–lag and its derivatives for the numerical solution of the Schrödinger equation, Comput. Math. Appl. 62 (2011) 3756–3774.##[10] A. Ibraheem, T. E. Simos, A family of ten–step methods with vanished phase–lag and its first derivative for the numerical solution of the Schrödinger equation, J. Math. Chem. 49 (2011) 1843–1888.##[11] A. Ibraheem, T. E. Simos, Mulitstep methods with vanished phase–lag and its first and second derivatives for the numerical integration of the Schrödinger equation, J. Math. Chem. 48 (2010) 1092–1143.##[12] L. Gr. Ixaru, M. Rizea, A Numerov–like scheme for the numerical solution of the Schrödinger equation in the deep continuum spectrum of energies, Comput. Phys. Commun. 19 (1) (1980) 23–27.##[13] M. K. Jain, R. K. Jain and U. Krishnaiah, Obrechkoff methods for periodic initial value problems of second order differential equations, J. Math. Phys. Sci. 15 (1981) 239–250.##[14] J. D. Lambert, I. A. Watson, Symmetric multistep methods for periodic initial value problems, IMA J. Appl. Math. 18 (1976) 189–202.##[15] G. D. Quinlan, S. Tremaine, Symmetric multistep methods for the numerical integration of planetary orbits, Astron. J. 100 (1990) 1694–1700.##[16] D. P. Sakas, T. E. Simos, Multiderivative methods of eighth algebraic order with minimal phase–lag for the numerical solution of the radial Schrödinger equation, J. Comput. Appl. Math. 175 (2005) 161–172.##[17] A. Shokri, H. Saadat, Trigonometrically fitted high–order predictor–corrector method with phase–lag of order infinity for the numerical solution of radial Schrödinger equation, J. Math. Chem. 52 (2014) 1870–1894.##[18] A. Shokri, H. Saadat, High phase–lag order trigonometrically fitted two–step Obrechkoff methods for the numerical solution of periodic initial value problems, Numer. Algor. 68 (2015) 337–354.##[19] A. Shokri, A. A. Shokri, Sh. Mostafavi, H. Saadat, Trigonometrically fitted twostep Obrechkoff methods for the numerical solution of periodic initial value problems, Iranian J. Math. Chem. 6 (2015) 145161.##[20] T. E. Simos, A Pstable complete in phase Obrechkoff trigonometric fitted method for periodic initial value problems, Proc. Roy. Soc. London Ser. A. 441 (1993) 283–289.##[21] T. E. Simos, A two–step method with vanished phase–lag and its first two derivatives for the numerical solution of the Schrödinger equation, J. Math. Chem. 49 (2011) 2486–2518.##[22] T. E. Simos, Exponentially fitted multiderivative methods for the numerical solution of the Schrödinger equation, J. Math. Chem. 36 (2004) 13–27.##[23] T. E. Simos, Multiderivative methods for the numerical solution of the Schrödinger equation, MATCH Commun. Math. Comput. Chem. 50 (2004) 7–26.##[24] E. Steifel, D. G. Bettis, Stabilization of Cowells methods, Numer. Math. 13 (1969) 154–175.##[25] R. M. Thomas, Phase properties of high order, almost P–stable formulae, BIT 24 (1984) 225–238.##[26] M. Van Daele, G. Vanden Berghe, Pstable exponentially fitted Obrechkoff methods of arbitrary order for second order differential equations, Numer. Algor. 46 (2007) 333–350.##[27] Z. Wang, D. Zhao, Y. Dai and D. Wu, An improved trigonometrically fitted P–stable Obrechkoff method for periodic initial value problems, Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 461 (2005) 1639–1658.##]
Optimal control of switched systems by a modified pseudo spectral method
2
2
In the present paper, we develop a modified pseudospectral scheme for solving an optimal control problem which is governed by a switched dynamical system. Many realworld processes such as chemical processes, automotive systems and manufacturing processes can be modeled as such systems. For this purpose, we replace the problem with an alternative optimal control problem in which the switching times appear as unknown parameters. Using the LegendreGaussLobatto quadrature and the corresponding differentiation matrix, the alternative problem is discretized to a nonlinear programming problem. At last, we examine three examples in order to illustrate the efficiency of the proposed method.
1

161
173


H.
Tabrizidooz
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan
Department of Applied Mathematics, Faculty
Iran
htabrizidooz@kashanu.ac.ir


M.
Pourbabaee
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan
Department of Applied Mathematics, Faculty
Iran
m.pourbabaee@kashanu.ac.ir


M.
Hedayati
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan
Department of Applied Mathematics, Faculty
Iran
mehrhedayati@yahoo.com
Optimal control
switched systems
Legendre pseudospectral method
[C. Canuto, M. Y. Hussaini, A. Quarteroni and T. A. Zang, Spectral Methods: Fundamentals in Single Domains, Springer–Verlag, Berlin, 2006.##B. Fornberg, A Practical Guide to Pseudospectral Methods, Cambridge University Press, 1996.##L. N. Trefethen, Spectral Methods in MATLAB, SIAM, Philadelphia, 2000.##D. E. Kirk, Optimal Control Theory, Prentice–Hall, Englewood Cliffs, New Jersey, 1970.##L. S. Pontryagin, V. Boltyanskii, R. Gamkrelidze and E. Mischenko, The Mathematical Theory of Optimal Processes, Interscience Publishers, New York, 1962.##C. P. Neuman and A. Sen, A suboptimal control algorithm for constrained problems using cubic splines, Automatica 9 (1973) 601–613.##J. Vlassenbroeck, A Chebyshev polynomial method for optimal control with state constraint, Automatica 24 (1988) 499–506.##J. Vlassenbroeck and R. Van Doreen, A Chebyshev technique for solving nonlinear optimal control problems, IEEE Trans. Automat. Control 33 (1988) 333–340.##C. J. Goh and K. L. Teo, Control parametrization: a unified approach to optimal control problems with general constraint, Automatica 24 (1988) 3–18.##O. Rosen and R. Luus, Evaluation of gradients for piecewise constraint optimal control, Computers and Chemical Engineering 15 (1991) 273–281.##W. W. Hager, Multiplier methods for nonlinear optimal control, SIAM J. Numer. Anal. 27 (1990) 1061–1080.##D. H. Jacobson and M. M. Lele, A Transformation technique for optimal control problems with a state variable inequality constraints, IEEE Trans. Automat. Control AC–14 (1969) 457–464.##E. Polak, T. H. Yang and D. Q. Mayne, A method of centers based on barrier function methods for solving optimal control problems with continuum state and control constraints, SIAM J. Control Optim. 31 (1993) 159–179.##G. N. Elnagar, M. A. Kazemi and M. Razzaghi, The pseudospectral Legendre method for discretizing optimal control problems, IEEE Trans. Automat. Control 40 (1995) 1793–1796.##G. N. Elnagar and M. A. Kazemi, Pseudospectral Chebyshev optimal control of constrained nonlinear dynamical systems, Comput. Optim. Appl. 11 (1998) 195–217.##F. Fahroo and I. M. Ross, Costate estimation by a Legendre pseudospectral method, J. Guid. Control Dyn. 24 (2001) 270–277.##G. T. Huntington, D. A. Benson and A. V. Rao, Post–optimality evaluation and analysis of a formation flying problem via a Gauss pseudospectral method, 2005, AAS paper no. 05–339.##Q. Gong, W. Kang and I. M. Ross, A pseudospectral method for the optimal control of constrained feedback linearizable systems, IEEE Trans. Automat. Control 51 (2006) 1115–1129.##M. Shamsi, A modified pseudospectral scheme for accurate solution of Bang–Bang optimal control problems, Optimal Control Appl. Methods 32 (2011) 668–680.##R. Fletcher, Practical Methods of Optimization, John Wiely, Chichester, 1987.##J. Nocedal and S. J. Wright, Numerical Optimization, Springer Series in Operations Research, Springer, New York, 1999.##I. M. Ross and F. Fahroo, Pseudospectral knotting methods for solving optimal control problems, J. Guid. Control Dyn. 27 (2004) 397–405.##I. E. Grossmann, S. A. Van Den Heever and I. Harjukoski, Discrete optimization methods and their role in the integration of planning and scheduling, AIChE Symposium Series 98 (2002) 150–168.##N. H. El–Farra, P. Mhaskar and P. D. Christofides, Feedback control of switched nonlinear systems using multiple Lyapunov functions, in Proceedings of American Control Conference, pages 3496–3502, Arlington, VA, 2001.##R. A. Decarlo, M. S. Branicky, S. Petterson and B. Lennartson, Perspectives and results on the stability and stabilizability of hybrid systems, Proceedings of the IEEE 88 (2000) 1069–1082.##A. Bemporad and M. Morari, Control of systems integrating logic, dynamics and constraints, Automatica 35 (1999) 407–427.##B. Hu, X. Xu, P. J. Antsaklis and A. N. Michel, Robust stabilizing control law for a class of second–order switched systems, Systems Control Lett. 38 (1999) 197–207.##N. H. El–Farra, P. Mhaskar and P. D. Christofides, Output feedback control of switched nonlinear systems using multiple Lyapunov functions, Systems Control Lett. 54 (2005) 1163–1182.##R. Ghosh and C. Tomlin, Symbolic reachable set computation of piecewise affine hybrid automata and its application to biological modelling: Delta–Notch protein signalling, Syst. Biol. 1 (2004) 170–183.##P. G. Howlett, P. J. Pudney and X. Vu, Local energy minimization in optimal train control, Automatica 45 (2009) 2692–2698.##S. Engell, S. Kowalewski, C. Schulz and O. Stursberg, Continuous–discrete interactions in chemical processing plants, Proceedings of the IEEE 88 (2000) 1050–1068.##C. Liu and Z. Gong, Optimal Control of Switched Systems Arising in Fermentation Processes, Springer–Verlag, Berlin Heidelberg, 2014.##X. Xu and P.J. Antsaklis, Optimal control of switched systems based on parameterization of the switching instants, IEEE Trans. Automat. control 49 (2004) 2–16.##P. J. Davis and P. Rabinowitz, Methods of Numerical Integration, Academic Press, New York, 1984.##]
Computing Szeged index of graphs on triples
2
2
ABSTRACT Let G=(V,E) be a simple connected graph with vertex set V and edge set E. The Szeged index of G is defined by where respectively is the number of vertices of G closer to u (respectively v) than v (respectively u). If S is a set of size let V be the set of all subsets of S of size 3. Then we define three types of intersection graphs with vertex set V. These graphs are denoted by and we will find their Szeged indices.
1

175
180


M.
Darafsheh
School of Mathematics, College of Science, University of Tehran
School of Mathematics, College of Science,
Iran
darafsheh@ut.ac.ir


R.
Modabernia
Department of Mathematics, Shahid Chamran University of Ahvaz
Department of Mathematics, Shahid Chamran
Iran
r.modabber@yahoo.com


M.
Namdari
Department of Mathematics, Shahid Chamran University of Ahvaz
Department of Mathematics, Shahid Chamran
Iran
namdari@ipm.ir
Szeged index
Intersection graph
Automorphism of graph
[M. R. Darafsheh, Computation of topological indices of some graphs, Acta. Appl. Math. 110 (2010) 1225–1235.##J. D. Dixon and B. Mortimer, Permutation Groups, Springer–Verley, NewYork, 1996.##M. Ghorbani, Computing the Wiener index of graphs on triples, Creat. Math. Inform. 24 (2015) no.1 49–52##I. Gutman, A formula for the Wiener number of trees and its extension to graphs containing cyclic, Graph Theory Notes NY. 27 (1994) 9–15.##I. Gutman and A. A. Dobrynin, The Szeged indexasuccess story, Graph Theory Notes NY. 34 (1998) 37–44.##H. Hosoya, Topological Index. A Newly Proposed Quantity Characterizing the Topological Nature of Structural Isomers of Saturated Hydrocarbons, Bull. Chem. Soc. Japan. 44 (1971) 2332–2339.##P. V. Khadikar, N. V. Deshpande, P. P. Kale, A. Dobrinin, I. Gutman and G. Domotor, The Szeged index and analogy with the Wiener index, J. Chem. Inf. Comput. Sci. 35 (1995) 547–550.##H. Wiener, Structural Determination of Paraffin Boiling Points, J. Am. Chem. Soc. 69 (1947) 17–20.##J. Zerovnik, Szeged index of symmetric graphs, J. Chem. Inf. Comput. Sci. 39 (1999) 77–80.##]
NordhausGaddum type results for the Harary index of graphs
2
2
The emph{Harary index} $H(G)$ of a connected graph $G$ is defined as $H(G)=sum_{u,vin V(G)}frac{1}{d_G(u,v)}$ where $d_G(u,v)$ is the distance between vertices $u$ and $v$ of $G$. The Steiner distance in a graph, introduced by Chartrand et al. in 1989, is a natural generalization of the concept of classical graph distance. For a connected graph $G$ of order at least $2$ and $Ssubseteq V(G)$, the emph{Steiner distance} $d_G(S)$ of the vertices of $S$ is the minimum size of a connected subgraph whose vertex set contains $S$. Recently, Furtula, Gutman, and Katani'{c} introduced the concept of Steiner Harary index and gave its chemical applications. The emph{$k$center Steiner Harary index} $SH_k(G)$ of $G$ is defined by $SH_k(G)=sum_{Ssubseteq V(G),S=k}frac{1}{d_G(S)}$. In this paper, we get the sharp upper and lower bounds for $SH_k(G)+SH_k(overline{G})$ and $SH_k(G)cdot SH_k(overline{G})$, valid for any connected graph $G$ whose complement $overline {G}$ is also connected.
1

181
198


Z.
Wang
Beijing Normal Unviersity
Beijing Normal Unviersity
P. R. China
wangzhao580@yahoo.com


Y.
Mao
Qinghai Normal Unviersity
Qinghai Normal Unviersity
P. R. China
maoyaping@ymail.com


X.
Wang
Qinghai Normal University
Qinghai Normal University
P. R. China
wangxiaia@163.com


C.
Wang
Qinghai Normal Unviersity
Qinghai Normal Unviersity
P. R. China
wangchunxiaia@163.com
Distance
Steiner distance
Harary index
Kcenter Steiner Harary index
[J. Akiyama, F. Harary, A graph and its complement with specified properties, Int. J. Math. Math. Sci. 2 (1979) 223–228.## M. Aouchiche, P. Hansen, A survey of Nordhaus–Gaddum type relations, Discrete Appl. Math. 161 (2013) 466–546.## P. Ali, P. Dankelmann, S. Mukwembi, Upper bounds on the Steiner diameter of a graph, Discrete Appl. Math. 160 (2012) 1845–1850.## A. T. Balaban, The Harary index of a graph, MATCH Commun. Math. Comput. Chem. 75 (2016) 243–245.## J. A. Bondy, U. S. R. Murty, Graph Theory, Springer, 2008.## F. Buckley, F. Harary, Distance in Graphs, Addison–Wesley, Redwood, 1990.## J. Cáceresa, A. Márquezb, M. L. Puertasa, Steiner distance and convexity in graphs, Eur. J. Combin. 29 (2008) 726–736.## G. Chartrand, O. R. Oellermann, S. Tian, H. B. Zou, Steiner distance in graphs, Časopis Pest. Mat. 114 (1989) 399–410.## P. Dankelmann, O. R. Oellermann, H. C. Swart, The average Steiner distance of a graph, J. Graph Theory 22 (1996) 15–22.## P. Dankelmann, H. C. Swart, O. R. Oellermann, On the average Steiner distance of graphs with prescribed properties, Discrete Appl. Math. 79 (1997) 91–103.## P. Dankelmann, R. Entringer, Average distance, minimum degree, and spanning trees, J. Graph Theory 33 (2000) 1–13.## P. Dankelmann, O. R. Oellermann, H. C. Swart, The average Steiner distance of a graph, J. Graph Theory 22 (1996) 15–22.## A. Dobrynin, R. Entringer, I. Gutman, Wiener index of trees: theory and application, Acta Appl. Math. 66 (2001) 211–249.## R. C. Entringer, D. E. Jackson, D. A. Snyder, Distance in graphs, Czech. Math. J. 26 (1976), 283–296.## B. Furtula, I. Gutman, V. Katanić, Threecenter Harary index and its applications, Iranian J. Math. Chem. 7 (1) (2016) 61–68.## M. R. Garey, D. S. Johnson, Computers and Intractability – A Guide to the Theory of NP−Completeness, Freeman, San Francisco, 1979, pp. 208–209.## W. Goddard, O. R. Oellermann, Distance in graphs, in: M. Dehmer (Ed.), Structural Analysis of Complex Networks, Birkhäuser, Dordrecht, 2011, pp. 49–72.## I. Gutman, B. Furtula, X. Li, Multicenter Wiener indices and their applications, J. Serb. Chem. Soc. 80 (2015) 1009–1017.## I. Gutman, S. Klavžar, B. Mohar (Eds.), Fifty years of the Wiener index, MATCH Commun. Math. Comput. Chem. 35 (1997) 1–159.## I. Gutman, O. E. Polansky, Mathematical Concepts in Organic Chemistry, Springer, Berlin, 1986.## X. Li, Y. Fan, The connectivity and the Harary index of a graph, Discrete Appl. Math. 181 (2015) 167–173.## X. Li, Y. Mao, I. Gutman, The Steiner Wiener index of a graph, Discuss. Math. Graph Theory 36 (2) (2016) 455–465.## X. Li, Y. Mao, I. Gutman, Inverse problem on the Steiner Wiener index, Discuss. Math. Graph Theory, in press.## B. Lučić, A. Miličević, S. Nikolić, N. Trinajstić, Harary indextwelve years later, Croat. Chem. Acta 75 (2002) 847–868.## Y. Mao, The Steiner diameter of a graph, Bull. Iranian Math. Soc. 43 (2) (2017) 439−454.## Y. Mao, Steiner Harary index, Kragujevac J. Math. 42 (1) (2018) 29−39.## Y. Mao, Z. Wang, I. Gutman, Steiner Wiener index of graph products, Trans. Combin. 5 (3) (2016) 39–50.##Y. Mao, Z. Wang, I. Gutman, H. Li, NordhausGaddumtype results for the Steiner Wiener index of graphs, Discrete Appl. Math. 219 (2017) 167−175.##O. R. Oellermann, S. Tian, Steiner centers in graphs, J. Graph Theory 14 (1990) 585–597.## D. H. Rouvray, Harry in the limelight: The life and times of Harry Wiener, in: D. H. Rouvray, R. B. King (Eds.), Topology in Chemistry — Discrete Mathematics of Molecules, Horwood, Chichester, 2002, pp. 1–15.## D. H. Rouvray, The rich legacy of half century of the Wiener index, in: D. H. Rouvray, R. B. King (Eds.), Topology in Chemistry — Discrete Mathematics of Molecules, Horwood, Chichester, 2002, pp. 16–37.## H. Wiener, Structural determination of paraffin boiling points, J. Am. Chem. Soc. 69 (1947) 17–20.## K. Xu, K. C. Das, N. Trinajstić, The Harary Index of a Graph, Springer, Heidelberg, 2015.## K. Xu, M. Liu, K. C. Das, I. Gutman, B. Furtula, A survey on graphs extremal with respect to distance–based topological indices, MATCH Commun. Math. Comput. Chem.71 (2014) 461–508.##]
Determination of critical properties of Alkanes derivatives using multiple linear regression
2
2
This study presents some mathematical methods for estimating the critical properties of 40 different types of alkanes and their derivatives including critical temperature, critical pressure and critical volume. This algorithm used QSPR modeling based on graph theory, several structural indices, and geometric descriptors of chemical compounds. Multiple linear regression was used to estimate the correlation between these critical properties and molecular descriptors using proper coefficients. To achieve this aim, the most appropriate molecular descriptors were chosen from among 11 structural and geometric descriptors in order to determine the critical properties of the intended molecules. The results showed that among all the proposed models to predict critical temperature, pressure and volume, a model including the combination of such descriptors as HyperWiener, Platt, MinZL is the most appropriate one.
1

199
220


E.
Mohammadinasab
Islamic Azad University of Arak Branch
Islamic Azad University of Arak Branch
Iran
esmohammadinasab@gmail.com
Alkanes
MLR
Critical Properties
QSPR
[R. T. Morison and R. Neilson Boyd, Organic Chemistry, Allyn & Bacon, 2003.##H. Wiener, Correlation of heats of isomerization and differences in heats of vaporization of isomers, among the paraffin hydrocarbons, J. Am. Chem. Soc. 69 (1947) 2636–2638.##A. A. Gakh, E. G. Gakh, B. G. Sumpter and D. W. Noid, Neural network–graph theory approach to the prediction of the physical properties of organic compounds, J. Chem. Inf. Comput. Sci. 34 (1994) 832–839.##O. Ivanciuć, The neural network MolNet prediction of alkane enthalpies, Anal. Chem. Acta. 384 (1999) 271–284.##D. C. Montgomery, E. A. Peck and G. G. Vining, Introduction to Linear Regression Analysis, John Wiley & Sons, Inc, 2006.##R. Todeschini and V. Consonni, Handbook of Molecular Descriptors, Methods and Principles in Medicinal Chemistry, Wiley–VCH Verlag GmbH, 2008.##I. Gutman and B. Furtula (eds), Novel Molecular Structure Descriptors–Theory and Applications I and II, University of Kragujevac and Faculty of Science Kragujevac, 2010.##I. Gutman, A formula for the Wiener number of trees and its extension to graphs containing cycles, Graph Theory Notes N. Y. 27 (1994) 9−15.##R. B. King, Chemical Applications of Topology and Graph Theory, Elsevier, Amsterdam, 1983.##I. Gutman and O. E. Polansky, Mathematical Concepts in Organic Chemistry,Springer–Verlag, Berlin, 1986.##M. Randić, Chemical Graph Theory–Facts and Fiction, NISCAIR–CSIR, India, 2003.##H. Wiener, Structural determination of paraffin boiling points, J. Am. Chem. Soc. 69 (1947) 17–20.##M. Randić, Quantitative Structure–property relationship: boiling points of planar 1009benzenoids, New. J. Chem. 20 (1996) 1001–1009.##M. Shamsipur, B. Hemmateenejad and M. Akhond, Highly Correlating Distance/Connectivity–Based Topological Indices. 1: QSPR Studies of Alkanes, Bull. Korean Chem. Soc. 25 (2004) 253–259.##H. Hosseini and F. Shafiei, Quantitative Structure Property Relationship Models for the Prediction of Gas Heat Capacity of Benzene Derivatives Using Topological Indices, MATCH Commun. Math. Comput. Chem. 75 (2016) 583–592.##M. Goodarzi and E. Mohammadinasab, Theoretical investigation of relationship between quantum chemical descriptors, topological indices, energy and electric moments of zig–zag polyhex carbon nanotubes TUHC6[2p,q] with various circumference [2p] and fixed lengths, Fullerenes, Nanotubes Carbon Nanostructures. 21 (2013) 102–112.##A. Alaghebandi and F. Shafiei, QSPR modeling of heat capacity, thermal energy and entropy of aliphatic aldehydes by using topological indices and MLR method, Iranian J. Math. Chem.7 (2016) 235–251.##M. Pashm Forush, F. Shafie and F. Dialamehpour, QSPR study on benzene derivatives to some physico chemical properties by using topological indices, Iranian J. Math. Chem.7(1) (2016) 93–110.##G. Cash, S. Klavžar and M Petkovsek, Three Methods for Calculation of the HyperWiener Index of Molecular Graphs, J. Chem. Inf. Comput. Sci. 42 (2002) 571–576.##X. Li and Y. Shi, A survey on the Randić index, MATCH Commun. Math. Comput. Chem. 59 (2008) 127–156.##M. Randić, Characterization of atoms, molecules and classes of molecules based on paths. enumerations, MATCH Commun. Math. Comput. Chem. 7 (1979) 5–64.##B. Liu and I. Gutman, On general Randić indices, MATCH Commun. Math. Comput. Chem. 58 (2007) 147–154.## M. Randić, Charactrization of molecular branching, J. Am. Chem. Soc. 97 (1975) 6609–6615.## A. T. Balaban and T. S. Balaban, New Vertex Invariant and topological indices of chemical graphs based on information on distance, J. Math. Chem. 8 (1991) 383–397.## A. T. Balaban, Topological index based on topological distances in molecular graph,Pure Appl. Chem. 55 (1983) 199–206.## K. C. Das, B. Zhou and N. Trinajstić, Bounds on Harary index, J. Math. Chem. (2009) 1377–1393.##www.chemicalize.org##M. Randić and S. C. Basak, Multiple regression analysis with optimal molecular descriptors,SAR QSAR Environ. Res. 11 (2000) 1–23.##G. A. F. Seber and C. J. Wild, Nonlinear Regression, Hoboken, NJ: Wiley–Interscience, 2003.##K. Roy and I. Mitra, On various metrics used fo r validation of predictive QSAR models with applications in virtual screening and focused library design, Comb. Chem. High Throughput Screen. 14 (2011) 450–474.##]
Some relations between Kekule structure and MorganVoyce polynomials
2
2
In this paper, Kekule structures of benzenoid chains are considered. It has been shown that the coefficients of a B_n (x) MorganVoyce polynomial equal to the number of kmatchings (m(G,k)) of a path graph which has N=2n+1 points. Furtermore, two relations are obtained between regularly zigzag nonbranched catacondensed benzenid chains and MorganVoyce polynomials and between regularly zigzag nonbranched catacondensed benzenid chains and their corresponding caterpillar trees.
1

221
229


I.
Gultekin
Ataturk University
Ataturk University
Turkey
igultekin@atauni.edu.tr


B.
Sahin
bayburt university
bayburt university
Turkey
shnbnymn25@gmail.com
Kekule structure
Hosoya Index
MorganVoyce polynomial
Caterpillar Tree
[R. Tošić, I. Stojmenović, Chemical graphs, Kekulé structures and Fibonacci numbers, Zb. Rad. Prirod.–Mat. Fak. Ser. Mat. 25 (2) (1995) 179–195.##A. T. Balaban, I. Tomescu, Algebratic expressions for the number of Kekulé structure of isoarithmic cata–condensed benzenoid polycyclic hydrocarbons, MATCH Commun. Math. Comput. Chem. 14 (1983) 155–182.##H. Hosoya, Topological index. A newly proposed quantity characterizing the topological nature of structural isomers of saturated hydrocarbons, Bull. Chem. Soc. Jpn. 44 (1971) 2332–2339.##H. Hosoya, Topological index and Fibonacci numbers with relation to chemistry, Fibonacci Quart.11 (1973) 255–269.##H. Hosoya, Graphical and combinatorial aspects of some orthogonal polynomials, Natur. Sci. Rep. Ochanomizu Univ. 32 (2) (1981) 127–138.##I. Gutman, Topological properties of benzenoid systems. An identity for the sextet polynomial, Theor. Chim. Acta 45 (1977) 309–315.##H. Hosoya, I. Gutman, Kekulé structures of hexagonal chains–some unusual connections, J. Math. Chem. 44 (2008) 559–568.##T. Koshy, Fibonacci and Lucas numbers with applications, Pure and Applied Mathematics (New York), Wiley–Interscience, New York, 2001.##W. J. He, W. C. He, S. L. Xie, Algebratic expressions for Kekulé structure counts of nonbranched cata–condensed benzenoid, Discrete Appl. Math. 35 (1992) 91–106.##R. L. Graham, D. E. Knuth, O. Patashnik, Concrete Mathematics. A Foundation for Computer Science, Addison–Wesley, Reading, 1989.##]