THE MOSTAR INDEX OF FULLERENES IN TERMS OF AUTOMORPHISM GROUP

Abstract

Let $G$ be a connected graph. For an edge $e=uv\in E(G)$, suppose $n(u)$ and $n(v)$ are respectively, the number of vertices of $G$ lying closer to vertex $u$ than to vertex $v$ and the number of vertices of $G$ lying closer to vertex $v$ than to vertex $u$. The Mostar index is a topological index which is defined as $Mo(G)=\sum_{e\in E(G)}f(e)$, where $f(e) = |n(u)-n(v)|$. In this paper, we will compute the Mostar index of a family of fullerene graphs in terms of the automorphism group.