Iranian Journal of Mathematical Chemistry
Year:2017 | Volume:8 | Issue:1 |Papers Count:9

We show how generalized Zagreb indices M1 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.

Suppose G is a graph, A(G) its adjacency matrix and Ψ (G, λ ) = λ n + a1λ n− 1 + … +an is the characteristic polynomial of G. The matching polynomial of G is defined as M(G, x) = m(G, 0)xn – m(G, 1)xn− 2 – m(G, 2)xn− 4 + … , where m(G, k) is the number of k− matchings in G. In this paper, the relationship between 2k-th coefficient of the characteristic polynomial, a2k, and k-th coefficient of the matching polynomial, (− 1)km(G, k), k=0, 1, 2, … , in a regular graph is determined. In addition, these relations for finding 5, 6-matchings of fullerene graphs are applied.

In this paper, the Wiener and hyper Wiener indices of two kinds of dendrimer graphs are computed. Using the Wiener index formula, the Szeged, Schultz, PI and Gutman indices of these graphs are also determined.

Bucket recursive trees are an interesting and natural generalization of ordinary recursive trees and have a connection to mathematical chemistry. In this paper, we give the lower and upper bounds for the moment generating function and moments of the multiplicative Zagreb indices in a randomly chosen bucket recursive tree of size n with maximal bucket size b≥ 1. Also, we consider the ratio of the multiplicative Zagreb indices for different values of n and b. All our results reduce to the ordinary recursive trees for b =1.

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 been 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.

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.

Let G1 and G2 be simple connected graphs with disjoint vertex sets V(G1) and V(G2 ), respectively. For given vertices a1 ϵ V(G1) and a2 ϵ V(G2 ), a splice of G1 and G2 by vertices a1 and a2 is defined by identifying the vertices a1 and a2 in the union of G1 and G2. In this paper, we present exact formulas for computing some vertex-degree-based graph invariants of splice of graphs.

The first Zagreb index M1(G) is equal to the sum of squares of the degrees of the vertices and the first Zagreb coindex ¯ M1(G) is equal to the sum of sums of vertex degrees of the pairs of non-adjacent vertices. Kovijanić Vukić ević and G. Popivoda (Iran. J. Math. Chem. 5 (2014) 19– 29)...

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 some distance based topological indices for D[G] in terms of G. Finally, these formulas are applied for several special kinds of graphs, such as, the complete graph, the path and the cycle.