University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 17 2 2026 06 01 Counterexamples to a Conjecture on the Mostar Index of a Graph and its Line Graph 129 136 115563 10.22052/ijmc.2026.257415.2052 EN Liju Alex Department of Applied Science‎, ‎Rajiv Gandhi Institute of Technology‎, ‎Kottayam-686501‎, ‎India Gopalapillai Indulal Department of Mathematics‎, ‎St.Aloysius College‎, ‎Edathua‎, ‎Alappuzha‎ -689573, ‎India Journal Article 2025 08 13 ‎The Mostar index is a distance-based topological index defined as a quantitative measure of distance balancedness and peripherality in graphs‎. ‎Recently‎, ‎in “An inequality for the Mostar index of line graphs of trees” [Commun‎. ‎Comb‎. ‎Optim‎. ‎(2005)‎, ‎doi‎: ‎10.22049/cco.2025.30201.2356]‎, ‎the following conjecture regarding the Mostar index of graphs and their line graphs was proposed:<br />‎ Let G be a simple connected graph on $n$ vertices‎. ‎Then‎ Mo(L_G)<= Mo(G).<br />‎where‎, ‎L_G denotes the line graph of the graph G‎. ‎In this paper‎, ‎counterexamples are presented to disprove the conjecture proposed in \cite{sardar2025inequality}‎. ‎We also prove that the conjecture is not true for an infinite family of graphs with fixed cyclomatic number $c$‎, ‎where $1 \le c\le 3$‎. Mostar Index‎ Graph line graph https://ijmc.kashanu.ac.ir/article_115563_2ff05a505767a9423b073bf4d67a7119.pdf