Maximum values of the edge Mostar index in tricyclic graphs

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.