Relations Between Second Geometric-Arithmetic Index and Second Atom-Bond Connectivity Index

摘要

The geometric-arithmetic and atom-bond connectivity indices are of interesting and applied indices in the chemical graph theory. Let G = (V, E) be a simple, undirected and connected graph with vertex set V and edge set E. The second geometric-arithmetic and second atom-bond connectivity indices of a graph G are defined as, GA_2(G) = ∑ from uv∈E(G) of (2(n_un_v)~(1/2))/(n_u + n_v), ABC_2(G) = ∑ from uv∈E(G) of ((n_u + n_v - 2)/(n_un_v))~(1/2), where n_u is the number of vertices of graph G lying closer to u and n_v is the number of vertices of graph G lying closer to v. In this paper, we intend to demonstrate the relations between second geometric-arithmetic index and second atom-bond connectivity index for general and special class of graphs.