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arXiv · 1904.04131

Computing the Mostar index in networks with applications to molecular graphs

Niko Tratnik
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Abstract

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 this paper, we generalize the definition of the Mostar index to weighted graphs and prove that the Mostar index of a weighted graph can be computed in terms of Mostar indices of weighted quotient graphs. As a consequence, we show that the Mostar index of a benzenoid system can be computed in sub-linear time with respect to the number of vertices. Finally, our method is applied to some benzenoid systems and to a fullerene patch.

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Niko Tratnik. 2019-04-08. Computing the Mostar index in networks with applications to molecular graphs. https://doi.org/10.22052/ijmc.2020.240316.1526

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