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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.16080 |
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| _version_ | 1866909595044151296 |
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| author | Priya Singh, Sanjay Kumar |
| author_facet | Priya Singh, Sanjay Kumar |
| contents | Let $R$ be a finite commutative ring with unity and $x$ be a non-zero element of $R$. In this paper, we calculate the spectrum and energy of the Cayley graph ${\rm Cay}(R,xR^{*})$, and also compute the energy of their compliment graph. Further, we give necessary and sufficient condition for Cayley graph ${\rm Cay}(R,xR^{*})$ to be Ramanujan. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_16080 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Spectral properties of Cayley graphs over finite commutative rings Priya Singh, Sanjay Kumar Combinatorics 05C50, 20C25 Let $R$ be a finite commutative ring with unity and $x$ be a non-zero element of $R$. In this paper, we calculate the spectrum and energy of the Cayley graph ${\rm Cay}(R,xR^{*})$, and also compute the energy of their compliment graph. Further, we give necessary and sufficient condition for Cayley graph ${\rm Cay}(R,xR^{*})$ to be Ramanujan. |
| title | Spectral properties of Cayley graphs over finite commutative rings |
| topic | Combinatorics 05C50, 20C25 |
| url | https://arxiv.org/abs/2406.16080 |