فهرست مطالب
Iranian Journal of Mathematical Chemistry
Volume:8 Issue: 3, Summer 2017
- تاریخ انتشار: 1396/06/29
- تعداد عناوین: 8
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Pages 231-257I was born in Zagreb (Croatia) on October 26, 1936. My parents were Regina (née Pavić) (April17, 1916, ZagrebMarch 9, 1992, Zagreb) and Cvjetko Trinajstić (September 9, 1913, VoloskoOctober 29, 1998, Richmond, Australia).Keywords: Chemical graph theory, mathematical chemistry, Nanad Trinajstic
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Pages 259-273The forgotten topological index of a molecular graph $G$ is defined as $F(G)=\sum_{v\in V(G)}d^{3}(v)$, where $d(u)$ denotes the degree of vertex $u$ in $G$. The first through the sixth smallest forgotten indices among all trees, the first through the third smallest forgotten indices among all connected graph with cyclomatic number $\gamma=1,2$, the first through the fourth for $\gamma=3$, and the first and the second for $\gamma=4,5$ are determined. These results are compared with those obtained for the first Zagreb index.Keywords: Forgotten topological index, Unicyclic graphs, Bicyclic graphs, Tricyclic graphs, Tetracyclic graphs, Pentacyclic graphs
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Pages 275-283ýThe first variable Zagreb index of graph $G$ is defined asý ý\begin{eqnarray*}ý ýM_{1,\lambda}(G)=\sum_{v\in V(G)}d(v)^{2\lambda}ý, ý\end{eqnarray*}ý ýwhere $\lambda$ is a real number and $d(v)$ is the degree ofý ývertex $v$ý. ýIn this paperý, ýsome upper and lower bounds for the distribution function and expected value of this index in random increasing trees (recursive treesý, ýplane-oriented recursive trees and binary increasing trees) areý ýgivený.Keywords: First variable Zagreb index?, ?Random increasing? ?trees?, ?Distribution function?, ?Expected value
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Pages 285-290For 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.Keywords: Degree-Kirchhoff index, Laplacian matrix
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Pages 291-298Let 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.Keywords: Reduced distance matrix, Generalized Bethe Tree, Spectrum
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On the second order first zagreb indexPages 299-311Inspired by the chemical applications of higher-order connectivity index (or Randic index), we consider here the higher-order first Zagreb index of a molecular graph. In this paper, we study the linear regression analysis of the second order first Zagreb index with the entropy and acentric factor of an octane isomers. The linear model,based on the second order first Zagreb index, is better than models corresponding to the first Zagreb index and F-index. Further, we compute the second order first Zagreb index of line graphs of subdivision graphs of 2D-lattice, nanotube and nanotorus of TUC4C8[p; q], tadpole graphs, wheel graphs and ladder graphs.Keywords: Topological index, line graph, subdivision graph, nanostructure, tadpole graph
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Pages 313-325Let $G=(V,E)$ be a simple connected graph. A perfect matching (or Kekule 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 their anti-forcing numbers.Keywords: Anti-forcing number, Anti-forcing set, Corona product
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Pages 327-338The 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.Keywords: Zagreb indices, Forgotten index, Graph products