eng University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 2008-9015 2015-10-01 6 2 93 102 10.22052/ijmc.2015.10106 10106 M-polynomial and degree-based topological indices E. Deutsch emericdeutsch@msn.com 1 S. Klavžar sandi.klavzar@fmf.uni-lj.si 2 Polytechnic Institute of New York University Faculty of Mathematics and Physics, University of Ljubljana, Slovenia Let \$G\$ be a graph and let \$m_{ij}(G)\$, \$i,jge 1\$, be the number of edges \$uv\$ of \$G\$ such that \${d_v(G), d_u(G)} = {i,j}\$. The {em \$M\$-polynomial} of \$G\$ is introduced with \$displaystyle{M(G;x,y) = sum_{ile j} m_{ij}(G)x^iy^j}\$. It is shown that degree-based topological indices can be routinely computed from the polynomial, thus reducing the problem of their determination in each particular case to the single problem of determining the \$M\$-polynomial. The new approach is also illustrated with examples. http://ijmc.kashanu.ac.ir/article_10106_9757adf6f41e068e07ffdc82bc9d1b38.pdf Degree-based topological index Zagreb index Randic index Graph polynomial eng University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 2008-9015 2015-10-01 6 2 103 108 10.22052/ijmc.2015.10107 10107 Edge-decomposition of topological indices I. Gutman gutman@kg.ac.rs 1 Faculty of Science, University of Kragujevac, Kragujevac, Serbia The topological indices, defined as the sum of contributions of all pairs of vertices (among which are the Wiener, Harary, hyper–Wiener indices, degree distance, and many others), are expressed in terms of contributions of edges and pairs of edges. http://ijmc.kashanu.ac.ir/article_10107_7219f11930f0bb2a7a243517ae34b7d6.pdf topological index Molecular Graph edge-decomposition coindex eng University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 2008-9015 2015-10-01 6 2 109 119 10.22052/ijmc.2015.10410 10410 Photoluminescence quantitative analysis of Gallic acid and Caffeine in green tea using multi-way chemometric approaches S. Masoum masoum@kashanu.ac.ir 1 S. Heshmat sh.heshmat@gmail.com 2 Department of Analytical Chemistry, Faculty of Chemistry, University of Kashan, Kashan, I.R. Iran Department of Analytical Chemistry, Faculty of Chemistry, University of Kashan, Kashan, I.R. Iran Green tea is considered as a dietary source of antioxidant nutrients, which acts upon human health. Green tea leaves contain three main components in the form of simple hydroxy benzoic acids such as gallic acid, propyl gallate and xanthic bases (caffeine), have been reported to prevent or delay a number of degenerative diseases and act mainly upon the central nervous system and stimulating wakefulness. Therefore, it is important to establish a simple and reliable analytical method for determination of these compounds in the presence of unexpected interferences in the green tea sample. In this research, a rapid and sensitive method was used for the direct determination of gallic acid and caffeine in green tea that is based on excitation-emission data using chemometric approaches. Multi-way chemometric models can be used to study such data, providing estimates of the spectra and concentration profiles of the underlying chemical analytes. A high percentage of recoveries for the spiked green tea for gallic acid (i.e. 96.15 %-109.78 %) and caffeine (i.e. 93.75% -101.57%) indicate the high accuracies of the proposed calibration methods for the assessment of gallic acid and caffeine in green tea http://ijmc.kashanu.ac.ir/article_10410_93e154715e1cdd857466860b3bf7ca62.pdf Green tea Spectrofluorimetric analysis Excitation-emission data Three-way chemometric methods eng University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 2008-9015 2015-10-01 6 2 121 128 10.22052/ijmc.2015.10427 10427 The maximal total irregularity of some connected graphs M. Eliasi eliasi@math.iut.ac.ir 1 The total irregularity of a graph G is defined as 〖irr〗_t (G)=1/2 ∑_(u,v∈V(G))▒〖|d_u-d_v |〗, where d_u denotes the degree of a vertex u∈V(G). In this paper by using the Gini index, we obtain the ordering of the total irregularity index for some classes of connected graphs, with the same number of vertices. http://ijmc.kashanu.ac.ir/article_10427_9fae099b55610cd9a9d16305077bd5a4.pdf Total irregularity index Gini index majorization Trees Unicyclic graphs bicyclic graph eng University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 2008-9015 2015-10-01 6 2 129 135 10.22052/ijmc.2015.10428 10428 The reliability Wiener number of cartesian product graphs D. Rupnik Poklukar darja.rupnik@fs.uni-lj.si 1 J. Zerovnik janez.zerovnik@fs.uni-lj.si 2 University of Ljubljana University of Ljubljana Reliability Wiener number is a modification of the original Wiener number in which probabilities are assigned to edges yielding a natural model in which there are some (or all) bonds in the molecule that are not static. Various probabilities naturally allow modelling different types of chemical bonds because chemical bonds are of different types and it is well-known that under certain conditions the bonds can break with certain probability. This is fully taken into account in quantum chemistry. In the model considered here, probabilistic nature is taken into account and at the same time the conceptual simplicity of the discrete graph theoretical model is preserved. Here we extend previous studies by deriving a formula for the reliability Wiener number of a Cartesian product of graphs. http://ijmc.kashanu.ac.ir/article_10428_07180c1016b1b2b03841010eac54b78f.pdf Reliability Wiener number Wiener index Cartesian product of graphs eng University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 2008-9015 2015-10-01 6 2 137 143 10.22052/ijmc.2015.10429 10429 A note on connectivity and lambda-modified Wiener index W. Gao gaowei@ynnu.edu.cn 1 Y. Gao gaoyun@ynnu.edu.cn 2 Yunnan normal university yunnan normal university In theoretical chemistry, -modified Wiener index is a graph invariant topological index to analyze the chemical properties of molecular structure. In this note, we determine the minimum -modified Wiener index of graph with fixed connectivity or edge-connectivity. Our results also present the sufficient and necessary condition for reaching the lower bound. http://ijmc.kashanu.ac.ir/article_10429_01579a1608e80d4c9c5ad2257762be5e.pdf Chemical graph theory lambda-modified Wiener index connectivity Edge-connectivity eng University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 2008-9015 2015-10-01 6 2 145 161 10.22052/ijmc.2015.10451 10451 Trigonometrically fitted two-step obrechkoff methods for the numerical solution of periodic initial value problems A. Shokri shokri2090@gmail.com 1 A. Shokri a-shokri@iau-ahar.ac.ir 2 Sh. Mostafavi shabnammostafavi_91@yahoo.com 3 H. Saadat hosein67saadat@yahoo.com 4 Department of Mathematics, Faculty of Basic Science, University of Maragheh, Maragheh, Iran. Department of Mathematics, Ahar Branch, Islamic Azad University, Ahar, Iran. Faculty of Mathematical Science, University of Maragheh, Maragheh, Iran. Department of Mathematics, Faculty of Basic Science, University of Maragheh, Maragheh, Iran In this paper, we present a new two-step trigonometrically fitted symmetric Obrechkoff method. The method is based on the symmetric two-step Obrechkoff method, with eighth algebraic order, high phase-lag order and is constructed to solve IVPs with periodic solutions such as orbital problems. We compare the new method to some recently constructed optimized methods from the literature. The numerical results obtained by the new method for some problems show its superiority in efficiency, accuracy and stability. http://ijmc.kashanu.ac.ir/article_10451_e37900e24a74b6f240f6b1f76209f4e0.pdf Obrechkoff methods Trigonometrically-fitting Initial value problems Symmetric multistep methods Oscillating solution eng University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 2008-9015 2015-10-01 6 2 163 168 10.22052/ijmc.2015.10479 10479 Hyper-tubes of hyper-cubes A. Parvan-Moldovan eurosocmathchem@gmail.com 1 M. Diudea diudea@gmail.com 2 Babes-Bolyai University, Cluj, Romania Babes-Bolyai University, Cluj, Romania Hyper-tubes consisting of hyper-cubes of n-dimensions were designed and formulas for substructures of vary dimensions established. http://ijmc.kashanu.ac.ir/article_10479_0a521af99de82678ff6a280a224f54a7.pdf Graph n-cube Hyper-tube Hyper-torus n-dimensional space eng University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 2008-9015 2015-10-01 6 2 169 184 10.22052/ijmc.2015.10843 10843 A nonstandard finite difference scheme for solving‎ ‎fractional-order model of HIV-1 infection of‎ ‎CD4^{+} t-cells S. Zibaei s.zibaei@stu.vru.ac.ir 1 M. Namjoo namjoo@vru.ac.ir 2 Department of Mathematics, School of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran Department of Mathematics, School of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran ‎In this paper‎, ‎we introduce fractional-order into a model of HIV-1 infection of CD4^+ T--cells‎. ‎We study the effect of ‎the changing the average number of viral particles \$N\$ with different sets of initial conditions on the dynamics of‎ ‎the presented model‎. ‎ ‎The nonstandard finite difference (NSFD) scheme is implemented‎ ‎to study the dynamic behaviors in the fractional--order HIV-1‎ ‎infection model.‎ ‎ ‎Numerical results show that the‎ ‎NSFD approach is easy to be implemented and accurated when applied to fractional-order HIV-1‎ ‎infection model. http://ijmc.kashanu.ac.ir/article_10843_596181178c783132f395514fe2e6bb51.pdf HIV-1 model‎ ‎Nonstandard finite difference scheme‎ ‎Fractional differential equations‎ ‎Grunwald-Letnikov derivative‎ ‎Stability eng University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 2008-9015 2015-10-01 6 2 185 187 10.22052/ijmc.2015.10844 10844 Open problems for equienergetic graphs I. Gutman gutman@kg.ac.rs 1 Faculty of Science, University of Kragujevac, Kragujevac, Serbia The energy of a graph is equal to the sum of the absolute values of its eigenvalues. Two graphs of the same order are said to be equienergetic if their energies are equal. We point out the following two open problems for equienergetic graphs. (1) Although it is known that there are numerous pairs of equienergetic, non-cospectral trees, it is not known how to systematically construct any such pair. (2) If by numerical calculation one finds that two non-cospectral graphs seem to be equienergetic, in the general case no method is known for proving that this indeed is the case. http://ijmc.kashanu.ac.ir/article_10844_d32b4f131b209f2425a4517b4c86a2cb.pdf Graph energy equienergetic graphs Spectrum (of graph)