QSPR Analysis with Curvilinear Regression Modeling and Topological Indices

Document Type: Review Article


Mersin University



Topological indices are the real number of a molecular structure obtained via molecular graph G. Topological indices are used for QSPR, QSAR and structural design in chemistry, nanotechnology, and pharmacology. Moreover, physicochemical properties such as the boiling point, the enthalpy of vaporization, and stability can be estimated by QSAR/QSPR models. In this study, the QSPR (Quantitative Structure-Property Relationship) models were designed using the Gutman index, the product connectivity Banhatti index, the Variance of degree index, and the Sigma index to predict the thermodynamic properties of monocarboxylic acids. The relationship analyses between the thermodynamic properties and the topological indices were done by using the curvilinear regression method. It is used with the linear, quadratic and cubic equations of the curvilinear regression model. These regression models were then compared.



  1. F. K. Bell, A note on the irregularity of graphs, Linear Algebra Appl. 161 (1992) 45–54.
  2. G. Chartrand and L. Lesniak, Graphs and Digraphs, CRS Press, 2005.
  3. V. Consonni, D. Ballabio and R. Todeschini, Comments on the definition of the Q2 parameter for QSAR validation, J. Chem. Inf. Model. 49 (7) (2009) 1669–1678.
  4. J. C. Dearden, Advances in QSAR Modeling, Springer International Publishing, Switzerland, 2017.
  5. I. Gutman, A property of the simple topological index, MATCH Commun. Math. Comput. Chem. 25 (1990) 131–140.
  6. I. Gutman, M. Togan, A. Yurttas, A. S. Cevik and I. N. Cangul, Inverse problem for sigma index, MATCH Commun. Math. Comput. Chem. 79 (2018) 491–508.
  7. I. Gutman, Selected properties of Schultz molecular topological index, J. Chem. Inf. Coumput. Sci. 34 (1994) 1087–1089.
  8. S. Hosamani, D. Perigidad, S. Jamagoud, Y. Maled and S. Gavade, QSPR analysis of certain degree based topological indices, J. Stat. Appl. Prob. 6 (2017) 361–371.
  9. 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.
  10. H. Hosseini and F. Shafiei, Entropy prediction of benzene derivatives using topological indices, Studia UBB Chemia LXII, 2 (2017) 297–310.
  11. P. V. Khadikar and S. Karmarkar, A novel PI index and its applications to QSPR/QSAR studies, J. Chem. Info. Comp. Sci.41 (2001) 934–949.
  12. V. R. Kulli, B. Chaluvaraju and H. S. Boregowda, The product connectivity Banhatti index of a graph, Dis. Math. Graph Theory 39 (2019) 505–517.
  13. E. Mohammadinasab, Determination of critical properties of Alkanes derivatives using multiple linear regressions, Iranian J. Math. Chem. 8 (2017) 199–220.
  14. F. Shafiei, Relationship between Topological indices and Thermodynamic properties and of the Monocarboxylic acids Applications in QSPR, Iranian J. Math. Chem. 6 (2015) 15–28.
  15. N. Sivaraman, T. G. Srinivasan and P. R. Vasudeva Rao, QSPR modeling for solubility of fullerene (C60) in organic solvents, J. Chem. Inf. Comput. Sci. 41 (2001) 1067–1074.
  16. R. Todeschini, Useful and unuseful summaries of regression Models, 2010. http://www.moleculardescriptors.eu/tutorials/T5_moleculardescriptors_models.pdf. (Access date: 23.06.2018).
  17. H. Wiener, Structural determination of paraffin boiling points, J. Am. Chem. Soc. 69 (1947) 17–20.