THE REVISED EDGE SZEGED INDEX OF BRIDGE GRAPHS

Abstract

The revised edge Szeged index of a connected graph G is defined as Sz∗ e (G) = X e=uv∈E(G) mu(e|G) + m0(e|G) 2 mv(e|G) + m0(e|G) 2 , where E(G) is the edge set of G, mu(e|G) is the number of edges closer to vertex u than to vertex v in G, mv(e|G) is the number of edges closer to vertex v than to vertex u in G, and m0(e|G) is the number of edges equidistant from both ends of e. We give a formula for the revised edge Szeged index of a bridge graph, from which the revised edge Szeged indices for several classes of graphs are calculated.