فهرست مطالب

Mathematical Chemistry - Volume:8 Issue: 1, Winter 2017

Iranian Journal of Mathematical Chemistry
Volume:8 Issue: 1, Winter 2017

  • تاریخ انتشار: 1395/11/16
  • تعداد عناوین: 9
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  • T. Doslic, S. Sedghi *, N. Shobe Pages 1-5
    We show how generalized Zagreb indices $M_1^k(G)$ can be computed by using a simple graph polynomial and Stirling numbers of the second kind. In that way we explain and clarify the meaning of a triangle of numbers used to establish the same result in an earlier reference.
    Keywords: Simple Graph, Zagreb index, Stirling number
  • G. H. Fath Tabar *, F. Taghvaee Pages 7-23
    Suppose G is a graph, A(G) its adjacency matrix and f(G, x)=x^n_(n-1)x^(n-1)... is the characteristic polynomial of G. The matching polynomial of G is defined as M(G, x) = x^n-m(G,1)x^(n-2) ... where m(G,k) is the number of k-matchings in G. In this paper, we determine the relationship between 2k-th coefficient of characteristic polynomial, a_(2k), and k-th coefficient of matching polynomial, (-1)^km(G, k), in a regular graph. In the rest of this paper, we apply these relations for finding 5,6-matchings of fullerene graphs.
    Keywords: Characteristic polynomial, matching polynomial, fullerene graphs
  • M. R. Darafsheh, M. Namdari, S. Shokrolahi * Pages 25-35
    In this paper the Wiener and hyper Wiener index of two kinds of dendrimer graphs are determined. Using the Wiener index formula, the Szeged, Schultz, PI and Gutman indices of these graphs are also determined.
    Keywords: Topological index, Dendrimer, Wiener index, hyper Wiener index
  • R. Kazemi * Pages 37-45
    ýBucket recursive trees are an interesting and naturalý ýgeneralization of ordinary recursive trees and have a connectioný to mathematical chemistryý. ýIn this paperý, ýwe give the lower and upper bounds for the moment generatingý ýfunction and moments of the multiplicative Zagreb indices in aý ýrandomly chosen bucket recursive tree of size $n$ with maximal bucket size $bgeq1$ý. Also, ýwe consider the ratio of the multiplicative Zagrebý ýindices for different values of $n$ and $b$ý. ýAll our results reduce to the ordinary recursive trees for $b=1$ý.
    Keywords: Bucket recursive trees?, ?the multiplicative Zagreb indices?, ?moment generating? ?function?, ?moments
  • M. Torabi Rad, A. Abbasi * Pages 47-52
    Le Chatelier's principle is used as a very simple way to predict the effect of a change in conditions on a chemical equilibrium. . However, several studies have reported the violation of this principle, still there is no reported simple mathematical equation to express the exact condition of violation in the gas phase reactions. In this article, we derived a simple equation for the violation of Le Chatelier's principle for the ideal gas reactions at the constant temperature and pressure.
    Keywords: violation of Le Chatelier principle, Gas reaction, Equation of state, Mixture, Chemical equilibria
  • B. Basavanagoud *_S. Patil_V. R Desai_M. Tavakoli_A. R Ashrafi Pages 53-60
    A connected graph G is said to be neighbourly irregular graph if no two adjacent vertices of G have same degree. In this paper we obtain neighbourly irregular derived graphs such as semitotal-point graph, k^{tℎ} semitotal-point graph, semitotal-line graph, paraline graph, quasi-total graph and quasivertex-total graph and also neighbourly irregular of some graph products.
    Keywords: Neighbourly irregular, derived graphs, product graphs
  • Mahdieh Azari *, Farzaneh Falahati Nezhad Pages 61-70
    Let G_1 and G_2 be simple connected graphs with disjoint vertex sets V(G_1) and V(G_2), respectively. For given vertices a_1in V(G_1) and a_2in V(G_2), a splice of G_1 and G_2 by vertices a_1 and a_2 is defined by identifying the vertices a_1 and a_2 in the union of G_1 and G_2. In this paper, we present exact formulas for computing some vertex-degree-based graph invariants of splice of graphs.
    Keywords: Vertex degree, Graph invariant, Splice
  • R. Rasi, S. M. Sheikholeslami, A. Behmaram Page 71
    In this paper we give sharp upper bounds on the Zagreb indices and characterize all trees achieving equality in these bounds. Also, we give lower bound on first Zagreb coindex of trees.
    Keywords: first Zagreb index, first Zagreb coindex, tree, Chemical tree
  • M. K. Jamil Page 83
    Let $G$ be a connected graph, and let $D[G]$ denote the double graph of $G$. In this paper, we first derive closed-form formulas for different distance based topological indices for $D[G]$ in terms of that of $G$. Finally, as illustration examples, for several special kind of graphs, such as, the complete graph, the path, the cycle, etc., the explicit formulas for some distance based topological indices.
    Keywords: Wiener index, Harary index, Double graph