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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.17885 |
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| _version_ | 1866918115193913344 |
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| author | Borovićanin, Bojana Božović, Dragana Glogić, Edin Štesl, Daša Mesarič Špacapan, Simon Zogić, Emir |
| author_facet | Borovićanin, Bojana Božović, Dragana Glogić, Edin Štesl, Daša Mesarič Špacapan, Simon Zogić, Emir |
| contents | We study the Wiener index of a class of trees with fixed diameter and order. A double broom is a tree such that there exist two vertices $u$ and $v$, such that each leaf of $T$ is adjacent to $u$ or $v$. We prove that for a tree $T$ of diameter $d$ and (sufficiently large) order $n$ such that $n\leq d-2+4 \left\lfloor \sqrt{ \frac{d-1}{2}} \right\rfloor$, $T$ has maximum Wiener index (in the class of trees of diameter $d$ and order $n$) if and only if $T$ is a balanced double broom. Our results are sharp up to a small constant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_17885 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | New results on the Wiener index of trees with a given diameter Borovićanin, Bojana Božović, Dragana Glogić, Edin Štesl, Daša Mesarič Špacapan, Simon Zogić, Emir Combinatorics We study the Wiener index of a class of trees with fixed diameter and order. A double broom is a tree such that there exist two vertices $u$ and $v$, such that each leaf of $T$ is adjacent to $u$ or $v$. We prove that for a tree $T$ of diameter $d$ and (sufficiently large) order $n$ such that $n\leq d-2+4 \left\lfloor \sqrt{ \frac{d-1}{2}} \right\rfloor$, $T$ has maximum Wiener index (in the class of trees of diameter $d$ and order $n$) if and only if $T$ is a balanced double broom. Our results are sharp up to a small constant. |
| title | New results on the Wiener index of trees with a given diameter |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2507.17885 |