Eccentric Connectivity Index Of Molecular Grapgs Of Chemical Trees With Application To Alkynes

Abstract

Let G = (V,E) be a simple connected molecular graph. The eccentric connectivity index ξ (G) is a distance-based molecular structure descriptor that was recently used for mathematical modelling of biological activities of diverse nature. 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, v) be the notation of distance between vertices u, v ∈ V and is defined as the length of a shortest path connecting them. Then, the eccentricity connectivity index of a molecular graph Gis defined as ξ(G) = ∑ v∈V(G) deg(v)ec(v), where deg(v) (or simply dv ) is degree of a vertex v ∈ V (G), and is defined as the number of adjacent vertices with v. ec(v) is defined as the length of a maximal path connecting to another vertex of v. In this paper, we establish the general formulas for the eccentricity connectivity index of molecular graphs classes of chemical trees with applicatio