University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 14 2 2023 08 01 On a Conjecture on Edge Mostar Index of Bicyclic Graphs 97 108 113866 10.22052/ijmc.2023.248632.1680 EN Liju Alex Department of Mathematics, Bishop Chulaparambil Memorial College, Kottayam-686001 & Department of Mathematics, Marthoma College, Pathanamthitta - 689103, India Indulal Gopalapillai Department of Mathematics, St. Aloysius College, Edathua, Alappuzha - 689573, India Journal Article 2022 12 02 For an edge e = uv of a graph G, mu(e|G) denotes the number of edges closer<br />to the vertex u than to v (similarly mv(e|G)). The edge Mostar index Moe(G), of a graph<br />G is defined as the sum of absolute differences between mu(e|G) and mv(e|G) over all<br />edges e = uv of G. H. Liu et al. proposed a Conjecture on extremal bicyclic graphs with<br />respect to the edge Mostar index [1]. Even though the Conjecture was true in case of the<br />lower bound and proved in [2], it was wrong for the upper bound. In this paper, we<br />disprove the Conjecture proposed by H. Liu et al. [1], propose its correct version and<br />prove it. We also give an alternate proof for the lower bound of the edge Mostar index<br />for bicyclic graphs with a given number of vertices. https://ijmc.kashanu.ac.ir/article_113866_a4ed9d93b3ca02a832e1d847446b73c7.pdf