Integral Cayley graphs over a finite symmetric algebra
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913678318632960 |
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| author | Nguyen, Tung T. Tân, Nguyen Duy |
| author_facet | Nguyen, Tung T. Tân, Nguyen Duy |
| contents | A graph is called integral if its eigenvalues are integers. In this article, we provide the necessary and sufficient conditions for a Cayley graph over a finite symmetric algebra $R$ to be integral. This generalizes the work of So who studies the case where $R$ is the ring of integers modulo $n.$ We also explain some number-theoretic constructions of finite symmetric algebras arising from global fields, which we hope could pave the way for future studies on Paley graphs associated with a finite Hecke character. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_00307 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Integral Cayley graphs over a finite symmetric algebra Nguyen, Tung T. Tân, Nguyen Duy Number Theory Combinatorics 11R58, 05E40, 05C50 A graph is called integral if its eigenvalues are integers. In this article, we provide the necessary and sufficient conditions for a Cayley graph over a finite symmetric algebra $R$ to be integral. This generalizes the work of So who studies the case where $R$ is the ring of integers modulo $n.$ We also explain some number-theoretic constructions of finite symmetric algebras arising from global fields, which we hope could pave the way for future studies on Paley graphs associated with a finite Hecke character. |
| title | Integral Cayley graphs over a finite symmetric algebra |
| topic | Number Theory Combinatorics 11R58, 05E40, 05C50 |
| url | https://arxiv.org/abs/2411.00307 |