Extremal results on the Mostar index of trees with fixed parameters
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866913408422510592 |
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| author | Hayat, Fazal Xu, Shou-Jun |
| author_facet | Hayat, Fazal Xu, Shou-Jun |
| contents | For a graph $G$, the Mostar index of $G$ is the sum of $|n_u(e)$ - $n_v(e)|$ over all edges $e=uv$ of $G$, where $n_u(e)$ denotes the number of vertices of $G$ that have a smaller distance in $G$ to $u$ than to $v$, and analogously for $n_v(e)$. We determine all the graphs that maximize and minimize the Mostar index respectively over all trees in terms of some fixed parameters like the number of odd vertices, the number of vertices of degree two, and the number of pendent paths of fixed length. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_11328 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Extremal results on the Mostar index of trees with fixed parameters Hayat, Fazal Xu, Shou-Jun Combinatorics 05C12, 05C90 For a graph $G$, the Mostar index of $G$ is the sum of $|n_u(e)$ - $n_v(e)|$ over all edges $e=uv$ of $G$, where $n_u(e)$ denotes the number of vertices of $G$ that have a smaller distance in $G$ to $u$ than to $v$, and analogously for $n_v(e)$. We determine all the graphs that maximize and minimize the Mostar index respectively over all trees in terms of some fixed parameters like the number of odd vertices, the number of vertices of degree two, and the number of pendent paths of fixed length. |
| title | Extremal results on the Mostar index of trees with fixed parameters |
| topic | Combinatorics 05C12, 05C90 |
| url | https://arxiv.org/abs/2306.11328 |