The maximum atom-bond connectivity index for graphs with edge-connectivity one

摘要

The atom-bond connectivity (ABC) index of a graph G is defined as the sum of the weights root d(u)+d(v)-2/d(u)d(v) of all edges uv of G, where d(u) denotes the degree of a vertex u in G. In this short note, we determine the maximum ABC index for graphs with edge-connectivity one and characterize the corresponding extremal graphs. This answers a recent question proposed by Zhang et al. (2016). (C) 2016 Elsevier B.V. All rights reserved.