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

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

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