@article {
author = {Alex, Liju and Gopalapillai, Indulal},
title = {On a Conjecture on Edge Mostar Index of Bicyclic Graphs},
journal = {Iranian Journal of Mathematical Chemistry},
volume = {14},
number = {2},
pages = {97-108},
year = {2023},
publisher = {University of Kashan},
issn = {2228-6489},
eissn = {2008-9015},
doi = {10.22052/ijmc.2023.248632.1680},
abstract = {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.},
keywords = {topological index,Mostar index,Edge Mostar index,Bicyclic graphs},
url = {https://ijmc.kashanu.ac.ir/article_113866.html},
eprint = {https://ijmc.kashanu.ac.ir/article_113866_a4ed9d93b3ca02a832e1d847446b73c7.pdf}
}