University of KashanIranian Journal of Mathematical Chemistry2228-64898320170901Autobiographical notes2312574508710.22052/ijmc.2017.64354.1248ENN. TrinajstićThe Rugjer Bošković Institute and Croatian Academy of Sciences and Arts, Zagreb, CroatiaJournal Article20161028I was born in Zagreb (Croatia) on October 26, 1936. My parents were Regina (née Pavić) (April17, 1916, Zagreb–March 9, 1992, Zagreb) and Cvjetko Trinajstić (September 9, 1913, Volosko–October 29, 1998, Richmond, Australia).University of KashanIranian Journal of Mathematical Chemistry2228-64898320170901Graphs with smallest forgotten index2592734325810.22052/ijmc.2017.43258ENI. GutmanUniversity of Kragujevac, SerbiaA. GhalavandUniversity of KashanT. Dehghan-ZadehUniversity of KashanA. R.AshrafiUniversity of KashanJournal Article20160422The forgotten topological index of a molecular graph $G$ is<br /> defined as $F(G)=sum_{vin V(G)}d^{3}(v)$, where $d(u)$ denotes<br /> the degree of vertex $u$ in $G$. The first through the sixth smallest<br /> forgotten indices among all trees, the first through<br /> the third smallest forgotten indices among all connected<br /> graph with cyclomatic number $gamma=1,2$, the first through<br /> the fourth for $gamma=3$, and the first and the second for<br /> $gamma=4,5$ are determined. These results are compared<br /> with those obtained for the first Zagreb index.University of KashanIranian Journal of Mathematical Chemistry2228-64898320170901On the first variable Zagreb index2752834511310.22052/ijmc.2017.71544.1262ENK. MoradianDepartment of Statistics, Islamic Azad UniversityR. KazemiImam Khomeini international universityM. H.BehzadiDepartment of Statistics, Islamic Azad UniversityJournal Article20161229The first variable Zagreb index of graph $G$ is defined as<br /> begin{eqnarray*}<br /> M_{1,lambda}(G)=sum_{vin V(G)}d(v)^{2lambda},<br /> end{eqnarray*}<br /> where $lambda$ is a real number and $d(v)$ is the degree of<br /> vertex $v$.<br /> In this paper, some upper and lower bounds for the distribution function and expected value of this index in random increasing trees (recursive trees,<br /> plane-oriented recursive trees and binary increasing trees) are<br /> given.University of KashanIranian Journal of Mathematical Chemistry2228-64898320170901Computing the additive degree-Kirchhoff index with the Laplacian matrix2852904853210.22052/ijmc.2017.64656.1249ENJ. PalaciosThe University of New Mexico, Albuquerque, NM 87131, USAJournal Article20161102For any simple connected undirected graph, it is well known that the Kirchhoff and multiplicative degree-Kirchhoff indices can be computed using the Laplacian matrix. We show that the same is true for the additive degree-Kirchhoff index and give a compact Matlab program that computes all three Kirchhoffian indices with the Laplacian matrix as the only input.University of KashanIranian Journal of Mathematical Chemistry2228-64898320170901On the spectra of reduced distance matrix of the generalized Bethe trees2912984853310.22052/ijmc.2017.30051.1116ENA. HeydariArak University of TechnologyJournal Article20150608Let G be a simple connected graph and {v_1,v_2,..., v_k} be the set of pendent (vertices of degree one) vertices of G. The reduced distance matrix of G is a square matrix whose (i,j)-entry is the topological distance between v_i and v_j of G. In this paper, we compute the spectrum of the reduced distance matrix of the generalized Bethe trees.University of KashanIranian Journal of Mathematical Chemistry2228-64898320170901On the second order first zagreb index2993114978410.22052/ijmc.2017.83138.1284ENB BasavanagoudKARNATAK UNIVERSITY DHARWADS. PatilKarnatak UniversityH. Y. DengKey Laboratoryof High Performance Computing and Stochastic Information Processing, College of Mathematics and Computer Science, Hunan Normal University, Changsha, Hunan, 410081, P. R. ChinaJournal Article20170424Inspired by the chemical applications of higher-order connectivity index (or<br /> Randic index), we consider here the higher-order first Zagreb index of a molecular graph.<br /> In this paper, we study the linear regression analysis of the second order first Zagreb<br /> index with the entropy and acentric factor of an octane isomers. The linear model, based<br /> on the second order first Zagreb index, is better than models corresponding to the first<br /> Zagreb index and F-index. Further, we compute the second order first Zagreb index of<br /> line graphs of subdivision graphs of 2D-lattice, nanotube and nanotorus of TUC4C8[p; q],<br /> tadpole graphs, wheel graphs and ladder graphs.University of KashanIranian Journal of Mathematical Chemistry2228-64898320170901Anti-forcing number of some specific graphs3133254978510.22052/ijmc.2017.60978.1235ENS. AlikhaniYazd University, Yazd, IranN. SoltaniYazd UniversityJournal Article20160909Let $G=(V,E)$ be a simple connected graph. A perfect matching (or Kekul'e structure in chemical literature) of $G$ is a set of disjoint edges which covers all vertices of $G$. The anti-forcing number of $G$ is the smallest number of edges such that the remaining graph obtained by deleting these edges has a unique perfect matching and is denoted by $af(G)$. In this paper we consider some specific graphs that are of importance in chemistry and study <br /> their anti-forcing numbers.University of KashanIranian Journal of Mathematical Chemistry2228-64898320170901On the forgotten topological index3273384348110.22052/ijmc.2017.43481ENA. KhaksariDepartment of Mathematics, Payame Noor University, Tehran, 19395 – 3697, I. R. IranM. GhorbaniDepartment of mathematics, Shahid Rajaee Teacher Training UniversityJournal Article20160813The forgotten topological index is defined as sum of third power of degrees. In this paper, we compute some properties of forgotten index and then we determine it for some classes of product graphs.