The Upper Bound of the Edge Mostar Index with Respect to Bicyclic Graphs

Abstract

Let G be a connected graph; the edge Mostar index Moe(G) of G is defined as Moe(G)=∑e=uv∈E(G)|mu(e)−mv(e)|, where mu(e) and mv(e) denote the number of edges in G that are closer to vertex u than to vertex v and the number of edges that are closer to vertex v than to vertex u, respectively. In this paper, we determine the upper bound of the edge Mostar index for all bicyclic graphs and identify the extremal graphs that achieve this bound.