On minimum revised edge Szeged index of bicyclic graphs

Abstract

AbstractThe revised edge Szeged index [Formula: see text] of a graph G is defined as [Formula: see text] where [Formula: see text] and [Formula: see text] are, respectively, the number of edges of G lying closer to vertex u than to vertex v and the number of edges of G lying closer to vertex v than to vertex u, and [Formula: see text] is the number of edges equidistant to u and v. In the paper, we show the sharp lower bound of revised edge Szeged index regarding bicyclic graphs. Moreover, all extremal graphs are characterized.