Iranian Journal of Mathematical Chemistry
Volume:2 Issue: 2, Autumn-Winter 2011

A counting polynomial C(G, x) is a sequence description of a topological property so that the exponents express the extent of its partitions while the coefficients are related to the occurrence of these partitions. Basic definitions and properties of the Omega polynomial (G, x) and the Sadhana polynomial Sd(G, x) are presented. These polynomials for some infinite classes of fullerenes and nanotubes are also computed. The results of this paper are arranged according to the main Theorems of [9 43].

Distance-balanced graphs are introduced as graphs in which every edge uv has the following property: the number of vertices closer to u than to v is equal to the number of vertices closer to v than to u. Basic properties of these graphs are obtained. In this paper, we study the conditions under which some graph operations produce a distance-balanced graph.

Let G be a graph. The first Zagreb polynomial M1(G, x) and the third Zagreb polynomial M3(G, x) of the graph G are defined as: In this paper, we compute the first and third Zagreb polynomials of Cartesian product of two graphs and a type of dendrimers.

Let G be a molecular graph. The Wiener index of G is defined as the summation of all distances between vertices of G. In this paper, an exact formula for the Wiener index of a new type of nanostar dendrimer is given.

In this paper PI, Szeged and revised Szeged indices of an infinite family of IPR fullerenes with exactly 60+12n carbon atoms are computed. A GAP program is also presented that is useful for our calculations.

The first geometric-arithmetic index was introduced in the chemical theory as the summation of 2 du dv /(du  dv) overall edges of the graph, where du stand for the degree of the vertex u. In this paper we give the expressions for computing the first geometric-arithmetic index of hexagonal systems and phenylenes and present new method for describing hexagonal system by corresponding a simple graph to each hexagonal system.

The concept of geometric-arithmetic indices was introduced in the chemical graph theory. These indices are defined by the following general formula: where Qu is some quantity that in a unique manner can be associated with the vertex u of graph G. In this paper the exact formula for two types of geometric-arithmetic index of Vphenylenicnanotube are given.