Well-covered Unitary Cayley Graphs of Matrix Rings over Finite Fields and Applications
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909165742456832 |
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| author | Rahimi, Shahin Nikseresht, Ashkan |
| author_facet | Rahimi, Shahin Nikseresht, Ashkan |
| contents | Suppose that $F$ is a finite field and $R=M_n(F)$ is the ring of $n$-square matrices over $F$. Here we characterize when the Cayley graph of the additive group of $R$ with respect to the set of invertible elements of $R$, called the unitary Cayley graph of $R$, is well-covered. Then we apply this to characterize all finite rings with identity whose unitary Cayley graph is well-covered or Cohen-Macaulay. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2311_15255 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Well-covered Unitary Cayley Graphs of Matrix Rings over Finite Fields and Applications Rahimi, Shahin Nikseresht, Ashkan Combinatorics Commutative Algebra Rings and Algebras 05C25, 05C69, 15B33, 13H10 Suppose that $F$ is a finite field and $R=M_n(F)$ is the ring of $n$-square matrices over $F$. Here we characterize when the Cayley graph of the additive group of $R$ with respect to the set of invertible elements of $R$, called the unitary Cayley graph of $R$, is well-covered. Then we apply this to characterize all finite rings with identity whose unitary Cayley graph is well-covered or Cohen-Macaulay. |
| title | Well-covered Unitary Cayley Graphs of Matrix Rings over Finite Fields and Applications |
| topic | Combinatorics Commutative Algebra Rings and Algebras 05C25, 05C69, 15B33, 13H10 |
| url | https://arxiv.org/abs/2311.15255 |