On atom-bond connectivity index

Abstract

The atom-bond connectivity index (ABC) is a vertex-degree based graph invariant, put forward in the 1990s, having applications in chemistry. Let G = (V, E) be a graph, di the degree of its vertex i, and ij the edge connecting the vertices i and j. Then ABC =Σij{small element of}E√(di + dj-2)/(di dj). Upper bounds and Nordhaus-Gaddum type results for ABC are established.