Computing Eccentricity Connectivity Polynomial of Circumcoronene Series of Benzenoid H_k by Ring-Cut Method

Let G = (V,E) be a simple connected molecular graph. In such a simple molecular graph, vertices represent atoms and edges represent chemical bonds, we denoted the sets of vertices and edges by V = V (G) and E = E(G), respectively. If d(u, ν) be the notation of distance between vertices u, ν ∈ V and is defined as the length of a shortest path connecting them. Then, Eccentricity connectivity polynomial of a molecular graph G is defined as ECP(G, x) = ∑ν∈V ^d_G(ν)x^ecc(ν), where ecc(ν) is defined as the length of a maximal path connecting to another vertex of v. dG(ν) (or simply dv) is degree of a vertex ν ∈ V (G), and is defined as the number of adjacent vertices with v. In this paper, we focus on the structure of molecular graph circumcoronene series of benzenoid H_k (k ≥ 2) and counting the eccentricity connectivity polynomial ECP(H_k) and eccentricity connectivity index ξ(H_k), by new method (called Ring-cut Method).