On divisibility relation graphs
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911047490732032 |
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| author | Merzel, Jonathan L. Mináč, Ján Nguyen, Tung T. Tân, Nguyen Duy |
| author_facet | Merzel, Jonathan L. Mináč, Ján Nguyen, Tung T. Tân, Nguyen Duy |
| contents | For each positive integer $n$, we define the divisibility relation graph $D_n$ whose vertex set is the set of divisors of $n$, and in which two vertices are adjacent if one is a divisor of the other. This type of graph is a special case of graphs associated with a partial order, which have been widely studied in the literature. In this work, we determine various graph-theoretic invariants of divisibility relation graphs, such as their clique and independence numbers, and their planarity. We also discuss various spectral properties that are discovered by our numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_06873 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On divisibility relation graphs Merzel, Jonathan L. Mináč, Ján Nguyen, Tung T. Tân, Nguyen Duy Combinatorics 06A07, 05C25, 05C50 For each positive integer $n$, we define the divisibility relation graph $D_n$ whose vertex set is the set of divisors of $n$, and in which two vertices are adjacent if one is a divisor of the other. This type of graph is a special case of graphs associated with a partial order, which have been widely studied in the literature. In this work, we determine various graph-theoretic invariants of divisibility relation graphs, such as their clique and independence numbers, and their planarity. We also discuss various spectral properties that are discovered by our numerical experiments. |
| title | On divisibility relation graphs |
| topic | Combinatorics 06A07, 05C25, 05C50 |
| url | https://arxiv.org/abs/2507.06873 |