On gcd-graphs over finite rings
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866909527282024448 |
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| author | Nguyen, Tung T. Tân, Nguyen Duy |
| author_facet | Nguyen, Tung T. Tân, Nguyen Duy |
| contents | Gcd-graphs represent an interesting and historically important class of integral graphs. Since the pioneering work of Klotz and Sander, numerous incarnations of these graphs have been explored in the literature. In this article, we define and establish some foundational properties of gcd-graphs defined over a general finite commutative ring. In particular, we investigate the connectivity and diameter of these graphs. Additionally, when the ring is a finite symmetric $\mathbb{Z}/n$-algebra, we give an explicit description of their spectrum using the theory of Ramanujan sums that gives a unified treatment of various results in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_04086 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On gcd-graphs over finite rings Nguyen, Tung T. Tân, Nguyen Duy Number Theory Commutative Algebra Combinatorics Gcd-graphs represent an interesting and historically important class of integral graphs. Since the pioneering work of Klotz and Sander, numerous incarnations of these graphs have been explored in the literature. In this article, we define and establish some foundational properties of gcd-graphs defined over a general finite commutative ring. In particular, we investigate the connectivity and diameter of these graphs. Additionally, when the ring is a finite symmetric $\mathbb{Z}/n$-algebra, we give an explicit description of their spectrum using the theory of Ramanujan sums that gives a unified treatment of various results in the literature. |
| title | On gcd-graphs over finite rings |
| topic | Number Theory Commutative Algebra Combinatorics |
| url | https://arxiv.org/abs/2503.04086 |