The Upper Bound of the Edge Mostar Index with Respect to Bicyclic Graphs

Hui Wang and Mengmeng Liu ()
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Hui Wang: School of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, China
Mengmeng Liu: School of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, China

Mathematics, 2023, vol. 11, issue 11, 1-8

Abstract: Let G be a connected graph; the edge Mostar index M o e ( G ) of G is defined as M o e ( G ) = ∑ e = u v ∈ E ( G ) | m u ( e ) − m v ( e ) | , where m u ( e ) and m v ( e ) denote the number of edges in G that are closer to vertex u than to vertex v and the number of edges that are closer to vertex v than to vertex u , respectively. In this paper, we determine the upper bound of the edge Mostar index for all bicyclic graphs and identify the extremal graphs that achieve this bound.

Keywords: Mostar index; edge Mostar index; bicyclic graph (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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