Maximum values of the edge Mostar index in tricyclic graphs

TL;DR

This paper investigates the maximum possible edge Mostar index in tricyclic graphs, establishing a sharp upper bound and identifying the extremal graphs that achieve this maximum.

Contribution

It provides the first precise upper bound for the edge Mostar index in tricyclic graphs and characterizes the extremal graphs attaining this bound.

Findings

Established a sharp upper bound for the edge Mostar index in tricyclic graphs.

Identified the specific graphs that attain the maximum edge Mostar index.

Contributed to the extremal graph theory related to the edge Mostar index.

Abstract

For a graph $G$, the edge Mostar index of $G$ is the sum of $|m_u(e|G)-m_v(e|G)|$ over all edges $e=uv$ of $G$, where $m_u(e|G)$ denotes the number of edges of $G$ that have a smaller distance in $G$ to $u$ than to $v$, and analogously for $m_v(e|G)$. This paper mainly studies the problem of determining the graphs that maximize the edge Mostar index among tricyclic graphs. To be specific, we determine a sharp upper bound for the edge Mostar index on tricyclic graphs and identify the graphs that attain the bound.