The Neighbour Sum Problem on Trees
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912458732470272 |
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| author | Dutta, Sayan Gupta, Sohom |
| author_facet | Dutta, Sayan Gupta, Sohom |
| contents | A graph $\mathcal G = (\mathcal V, \mathcal E)$ is said to satisfy the Neighbour Sum Property if there exists some $f:\mathcal V\to\mathbb R$ such that $f\not\equiv 0$ and it maps every vertex to the sum of the values taken by its neighbours. In this article, we provide an algorithm to check whether a given finite tree satisfies the neighbour sum property. We also find a large class of trees on $n$ vertices that satisfy the property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_23965 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Neighbour Sum Problem on Trees Dutta, Sayan Gupta, Sohom Combinatorics Number Theory A graph $\mathcal G = (\mathcal V, \mathcal E)$ is said to satisfy the Neighbour Sum Property if there exists some $f:\mathcal V\to\mathbb R$ such that $f\not\equiv 0$ and it maps every vertex to the sum of the values taken by its neighbours. In this article, we provide an algorithm to check whether a given finite tree satisfies the neighbour sum property. We also find a large class of trees on $n$ vertices that satisfy the property. |
| title | The Neighbour Sum Problem on Trees |
| topic | Combinatorics Number Theory |
| url | https://arxiv.org/abs/2506.23965 |