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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.10830 |
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| _version_ | 1866911378861719552 |
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| author | Badawi, Ayman |
| author_facet | Badawi, Ayman |
| contents | Let $H$ be a finite abelian (commutative) group of order $n \geq 2$, and $m >1$ be an integer. We define the $m$-graph of $H$, denoted by $m-G(H)$, as a simple undirected graph with vertex set $H$, and two distinct vertices, $a, b \in H$, are connected by an edge if and only if $a^m = b$ or $b^m = a$. Several results regarding the properties of the $m$-$G(H)$ have been established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_10830 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the $m$-graph of a finite Abelian Group Badawi, Ayman Combinatorics 05C25, 05C05 Let $H$ be a finite abelian (commutative) group of order $n \geq 2$, and $m >1$ be an integer. We define the $m$-graph of $H$, denoted by $m-G(H)$, as a simple undirected graph with vertex set $H$, and two distinct vertices, $a, b \in H$, are connected by an edge if and only if $a^m = b$ or $b^m = a$. Several results regarding the properties of the $m$-$G(H)$ have been established. |
| title | On the $m$-graph of a finite Abelian Group |
| topic | Combinatorics 05C25, 05C05 |
| url | https://arxiv.org/abs/2601.10830 |