On the Graovac-Ghorbani index

Abstract

For the edge e = uv of a graph G, let nu = n(u|G) be the number of vertices of G lying closer to the vertex u than to the vertex v and nv= n(v|G) can be defined simailarly. Then the ABCGG index of G is defined as ABCGG =sum_{e=uv} sqrt{f(u,v)}, where f(u,v)= (nu+nv-2)/nunvThe aim of this paper is to give some new results on this graph invariant. We also calculate the ABCGG of an infinite family of fullerenes.