On the maximal Harary index of a class of bicyclic graphs

Abstract

Let G be a simple and connected graph, the Harary index of G, denoted by H(G), is defined as H(G) = Σ_u,v∈V(G) 1/d_G(u,v), where d_G(u, v) is the distance between u and v in G. Let B(n) be the set of bicyclic graphs with exactly two edge disjoint cycles. In this paper, we investigate the Harary index of bicyclic graphs in B(n) and characterize the bicyclic graphs with maximal Harary index.