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arXiv · 2103.04018

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

Hechao Liu·Lihua You·Hanlin Chen·Zikai Tang
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Abstract

Let $G =(V_{G}, E_{G})$ be a simple connected graph with its vertex set $V_{G}$ and edge set $E_{G}$. The Mostar index $Mo(G)$ was defined as $Mo(G)=\sum\limits_{e=uv\in E(G)}|n_{u}-n_{v}|$, where $n_{u}$ (resp., $n_{v}$) is the number of vertices whose distance to vertex $u$ (resp., $v$) is smaller than the distance to vertex $v$ (resp., $u$). In this study, we determine the first three minimum Mostar indices of tree-like phenylenes and characterize all the tree-like phenylenes attaining these values. At last, we give some numerical examples and discussion.

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Hechao Liu, Lihua You, Hanlin Chen, Zikai Tang. 2021-03-06. On the first three minimum Mostar indices of tree-like phenylenes. https://doi.org/10.1007/s12190-021-01677-9

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