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The atom-bond connectivity index of a graph G, denoted as ABC(G), is defined as the sum of the weight  sqrt((d u +d v -2)/d u d v ) of all edges uv of G, where du (or dv) denotes the degree of vertex u (or v) in G. The ABC index provides a good model for the stability of linear and branches alkanes as well as the strain energy of cycloalkanes. In this note, we prove that ABC index of a graph increases when two new edges are added.

Atom-bond connectivity index of graph with two edges added