On gcd-graphs over matrix rings
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917550597603328 |
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| author | Nguyen, Dung Nguyen, Tung T. |
| author_facet | Nguyen, Dung Nguyen, Tung T. |
| contents | Graphs defined over finite rings are well studied in the literature. The study of these graphs benefits from rich connections between several areas of mathematics, including number theory, algebra, combinatorics, and graph theory, and these connections often lead to interesting interactions between algebraic and combinatorial structures. In this article, we investigate gcd-graphs defined over matrix rings with coefficients in finite fields. We show that these graphs exhibit several interesting graph-theoretic properties. Along the way, we also prove some results on the structure of matrix rings, which may be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_00836 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On gcd-graphs over matrix rings Nguyen, Dung Nguyen, Tung T. Combinatorics 05C50, 15B33, 16S50 Graphs defined over finite rings are well studied in the literature. The study of these graphs benefits from rich connections between several areas of mathematics, including number theory, algebra, combinatorics, and graph theory, and these connections often lead to interesting interactions between algebraic and combinatorial structures. In this article, we investigate gcd-graphs defined over matrix rings with coefficients in finite fields. We show that these graphs exhibit several interesting graph-theoretic properties. Along the way, we also prove some results on the structure of matrix rings, which may be of independent interest. |
| title | On gcd-graphs over matrix rings |
| topic | Combinatorics 05C50, 15B33, 16S50 |
| url | https://arxiv.org/abs/2606.00836 |