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Computing the Mostar index in networks with applications to molecular graphs

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Niko Tratnik

Combinatorics · Submitted 8 Apr 2019

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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.

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arXiv ID1904.04131 (version 1)
Pith IDUXFNGIS2, Pith's permanent record of this paper and its review
CitationNiko Tratnik. "Computing the Mostar index in networks with applications to molecular graphs." arXiv:1904.04131 (2019). https://pith.science/paper/UXFNGIS2
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arXiv listing abstract v1. Results and the main claim are underlined; .

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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#sentencerolethe authors' own workstates the main conclusionstrength
s0 Recently, a bond-additive topological descriptor, named as the Mostar index, has been introduced as a measure of peripherality in networks. background 1.00 0.05 0.03 asserted 1.00
s1 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 $u$. background 0.98 0.10 0.04 asserted 1.00
s2 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. contribution 0.96 0.96 0.54 asserted 1.00
s3 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. result 0.93 0.95 0.42 asserted 1.00
s4 Finally, our method is applied to some benzenoid systems and to a fullerene patch. contribution 0.67 0.94 0.07 asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.62 · evidence from proof or derivation 1.00.

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The paper
Original 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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4 arXiv papers cite this in 10 sentences

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  • Inspired by the various successful topological descriptors of this type such as irregularity [ref] , Zagreb [ref] , PI [ref] , Szeged [ref] , revised-Szeged [ref] , and recently, another bond-additive topological descriptor, the Mostar index has been proposed by Došlic et. al in [ref] .

    Mostar index of graph operations · Introduction · 0.97

  • Moreover, the graph opration for the Mostar index were considered [ref] and the Mostar index was used to study properties of networks [ref] .

    On the first three minimum Mostar indices of tree-like phenylenes · Introduction · 0.96

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