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Recently, a bond-additive topological descriptor, named as the Mostar index,has been introduced as a measure of peripherality in networks. For a connectedgraph $G$, the Mostar index is defined as $Mo(G) = \sum_{e=uv \in E(G)} |n_u(e)- n_v(e)|$, where for an edge $e=uv$ we denote by $n_u(e)$ the number ofvertices of $G$ that are closer to $u$ than to $v$ and by $n_v(e)$ the numberof vertices of $G$ that are closer to $v$ than to $u$. In this paper, wegeneralize the definition of the Mostar index to weighted graphs and prove thatthe Mostar index of a weighted graph can be computed in terms of Mostar indicesof weighted quotient graphs. As a consequence, we show that the Mostar index ofa benzenoid system can be computed in sub-linear time with respect to thenumber of vertices. Finally, our method is applied to some benzenoid systemsand to a fullerene patch.

Computing the Mostar index in networks with applications to molecular graphs