%0 Journal Article
%T On a Conjecture on Edge Mostar Index of Bicyclic Graphs
%J Iranian Journal of Mathematical Chemistry
%I University of Kashan
%Z 2228-6489
%A Alex, Liju
%A Gopalapillai, Indulal
%D 2023
%\ 08/01/2023
%V 14
%N 2
%P 97-108
%! On a Conjecture on Edge Mostar Index of Bicyclic Graphs
%K topological index
%K Mostar index
%K Edge Mostar index
%K Bicyclic graphs
%R 10.22052/ijmc.2023.248632.1680
%X For an edge e = uv of a graph G, mu(e|G) denotes the number of edges closerto the vertex u than to v (similarly mv(e|G)). The edge Mostar index Moe(G), of a graphG is defined as the sum of absolute differences between mu(e|G) and mv(e|G) over alledges e = uv of G. H. Liu et al. proposed a Conjecture on extremal bicyclic graphs withrespect to the edge Mostar index [1]. Even though the Conjecture was true in case of thelower bound and proved in [2], it was wrong for the upper bound. In this paper, wedisprove the Conjecture proposed by H. Liu et al. [1], propose its correct version andprove it. We also give an alternate proof for the lower bound of the edge Mostar indexfor bicyclic graphs with a given number of vertices.
%U https://ijmc.kashanu.ac.ir/article_113866_a4ed9d93b3ca02a832e1d847446b73c7.pdf