M-polynomial and degree-based topological indices E. Deutsch Polytechnic Institute of New York University author S. Klavžar Faculty of Mathematics and Physics, University of Ljubljana, Slovenia author text article 2015 eng 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. Iranian Journal of Mathematical Chemistry University of Kashan 2228-6489 6 v. 2 no. 2015 93 102 http://ijmc.kashanu.ac.ir/article_10106_9757adf6f41e068e07ffdc82bc9d1b38.pdf dx.doi.org/10.22052/ijmc.2015.10106 Edge-decomposition of topological indices I. Gutman Faculty of Science, University of Kragujevac, Kragujevac, Serbia author text article 2015 eng 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. Iranian Journal of Mathematical Chemistry University of Kashan 2228-6489 6 v. 2 no. 2015 103 108 http://ijmc.kashanu.ac.ir/article_10107_7219f11930f0bb2a7a243517ae34b7d6.pdf dx.doi.org/10.22052/ijmc.2015.10107 Photoluminescence quantitative analysis of Gallic acid and Caffeine in green tea using multi-way chemometric approaches S. Masoum Department of Analytical Chemistry, Faculty of Chemistry, University of Kashan, Kashan, I.R. Iran author S. Heshmat Department of Analytical Chemistry, Faculty of Chemistry, University of Kashan, Kashan, I.R. Iran author text article 2015 eng 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 Iranian Journal of Mathematical Chemistry University of Kashan 2228-6489 6 v. 2 no. 2015 109 119 http://ijmc.kashanu.ac.ir/article_10410_93e154715e1cdd857466860b3bf7ca62.pdf dx.doi.org/10.22052/ijmc.2015.10410 The maximal total irregularity of some connected graphs M. Eliasi author text article 2015 eng 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. Iranian Journal of Mathematical Chemistry University of Kashan 2228-6489 6 v. 2 no. 2015 121 128 http://ijmc.kashanu.ac.ir/article_10427_9fae099b55610cd9a9d16305077bd5a4.pdf dx.doi.org/10.22052/ijmc.2015.10427 The reliability Wiener number of cartesian product graphs D. Rupnik Poklukar University of Ljubljana author J. Zerovnik University of Ljubljana author text article 2015 eng 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. Iranian Journal of Mathematical Chemistry University of Kashan 2228-6489 6 v. 2 no. 2015 129 135 http://ijmc.kashanu.ac.ir/article_10428_07180c1016b1b2b03841010eac54b78f.pdf dx.doi.org/10.22052/ijmc.2015.10428 A note on connectivity and lambda-modified Wiener index W. Gao Yunnan normal university author Y. Gao yunnan normal university author text article 2015 eng 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. Iranian Journal of Mathematical Chemistry University of Kashan 2228-6489 6 v. 2 no. 2015 137 143 http://ijmc.kashanu.ac.ir/article_10429_01579a1608e80d4c9c5ad2257762be5e.pdf dx.doi.org/10.22052/ijmc.2015.10429 Trigonometrically fitted two-step obrechkoff methods for the numerical solution of periodic initial value problems A. Shokri Department of Mathematics, Faculty of Basic Science, University of Maragheh, Maragheh, Iran. author A. Shokri Department of Mathematics, Ahar Branch, Islamic Azad University, Ahar, Iran. author Sh. Mostafavi Faculty of Mathematical Science, University of Maragheh, Maragheh, Iran. author H. Saadat Department of Mathematics, Faculty of Basic Science, University of Maragheh, Maragheh, Iran author text article 2015 eng 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. Iranian Journal of Mathematical Chemistry University of Kashan 2228-6489 6 v. 2 no. 2015 145 161 http://ijmc.kashanu.ac.ir/article_10451_e37900e24a74b6f240f6b1f76209f4e0.pdf dx.doi.org/10.22052/ijmc.2015.10451 Hyper-tubes of hyper-cubes A. Parvan-Moldovan Babes-Bolyai University, Cluj, Romania author M. Diudea Babes-Bolyai University, Cluj, Romania author text article 2015 eng Hyper-tubes consisting of hyper-cubes of n-dimensions were designed and formulas for substructures of vary dimensions established. Iranian Journal of Mathematical Chemistry University of Kashan 2228-6489 6 v. 2 no. 2015 163 168 http://ijmc.kashanu.ac.ir/article_10479_0a521af99de82678ff6a280a224f54a7.pdf dx.doi.org/10.22052/ijmc.2015.10479 A nonstandard finite difference scheme for solving‎ ‎fractional-order model of HIV-1 infection of‎ ‎CD4^{+} t-cells S. Zibaei Department of Mathematics, School of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran author M. Namjoo Department of Mathematics, School of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran author text article 2015 eng ‎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. Iranian Journal of Mathematical Chemistry University of Kashan 2228-6489 6 v. 2 no. 2015 169 184 http://ijmc.kashanu.ac.ir/article_10843_596181178c783132f395514fe2e6bb51.pdf dx.doi.org/10.22052/ijmc.2015.10843 Open problems for equienergetic graphs I. Gutman Faculty of Science, University of Kragujevac, Kragujevac, Serbia author text article 2015 eng 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. Iranian Journal of Mathematical Chemistry University of Kashan 2228-6489 6 v. 2 no. 2015 185 187 http://ijmc.kashanu.ac.ir/article_10844_d32b4f131b209f2425a4517b4c86a2cb.pdf dx.doi.org/10.22052/ijmc.2015.10844