University of Kashan Iranian Journal of Mathematical Chemistry 2228-6489 12 1 2021 03 01 Computing the Mostar Index in Networks with Applications to Molecular Graphs 1 18 111292 10.22052/ijmc.2020.240316.1526 EN Niko Tratnik University of Maribor, Faculty of Natural Sciences and Mathematics Journal Article 2020 10 09 Recently, a bond-additive topological descriptor, named as the Mostar index, has been introduced as a measure of peripherality in networks. For a connected graph $G$, 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 of vertices of $G$ that are closer to $u$ than to $v$ and by $n_v(e)$ the number of vertices of $G$ that are closer to $v$ than to $u$. In the present paper, we prove that the Mostar index of a weighted graph can be computed in terms of Mostar indices of weighted quotient graphs. Inspired by this result, several generalizations to other versions of the Mostar index already appeared in the literature. Furthermore, we apply the obtained method to benzenoid systems, tree-like polyphenyl systems, and to a fullerene patch. Closed-form formulas for two families of these molecular graphs are also deduced. https://ijmc.kashanu.ac.ir/article_111292_97ff81ab88f1726ca8516ec53cdfe05e.pdf