A lower bound on the Mostar index of tricyclic graphs

Abstract

For a  graph $G$, the Mostar index of $G$ is the sum of  $|n_{u}-n_{v}|$ over all edges $e=uv$ of $G$,  where $n_u$ denotes the number of vertices of $G$ that have a smaller distance in $G$ to $u$ than to $v$, and analogously for $n_v$. In this paper,  we obtain a lower bound for the Mostar index on tricyclic graphs and  identify those graphs that attain the lower bound.