A lower bound of revised Szeged index of bicyclic graphs

摘要

The revised Szeged index of a graph is defined as Sz*(G)=∑e=uv∈E(nu(e)+n0(e)2)(nv(e)+n0(e)2), where nu(e) and nv(e) are, respectively, the number of vertices of G lying closer to vertex u than to vertex v and the number of vertices of G lying closer to vertex v than to vertex u, and n0(e) is the number of vertices equidistant to u and v. In the paper, we identify the lower bound of revised Szeged index among all bicyclic graphs, and also characterize the extremal graphs that attain the lower bound.