TY - JOUR
ID - 113866
TI - On a Conjecture on Edge Mostar Index of Bicyclic Graphs
JO - Iranian Journal of Mathematical Chemistry
JA - IJMC
LA - en
SN - 2228-6489
AU - Alex, Liju
AU - Gopalapillai, Indulal
AD - Department of Mathematics, Bishop Chulaparambil Memorial College, Kottayam-686001
&
Department of Mathematics, Marthoma College, Pathanamthitta - 689103, India
AD - Department of Mathematics, St. Aloysius College, Edathua, Alappuzha - 689573, India
Y1 - 2023
PY - 2023
VL - 14
IS - 2
SP - 97
EP - 108
KW - topological index
KW - Mostar index
KW - Edge Mostar index
KW - Bicyclic graphs
DO - 10.22052/ijmc.2023.248632.1680
N2 - 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.
UR - https://ijmc.kashanu.ac.ir/article_113866.html
L1 - https://ijmc.kashanu.ac.ir/article_113866_a4ed9d93b3ca02a832e1d847446b73c7.pdf
ER -