A formula for eigenvalues of integral Cayley graphs over abelian groups
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929586392006656 |
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| author | Priya Kadyan, Monu |
| author_facet | Priya Kadyan, Monu |
| contents | Let $Z$ be an abelian group, $ x \in Z$, and $[x] = \{ y : \langle x \rangle = \langle y \rangle \}$. A graph is called integral if all its eigenvalues are integers. It is known that a Cayley graph is integral if and only if its connection set can be express as union of the sets $[x] $. In this paper, we determine an algebraic formula for eigenvalues of the integral Cayley graph when the connection set is $ [x]$. This formula involves an analogue of M$\ddot{\text{o}}$bius function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_06386 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A formula for eigenvalues of integral Cayley graphs over abelian groups Priya Kadyan, Monu Combinatorics 05C50, 20C15 Let $Z$ be an abelian group, $ x \in Z$, and $[x] = \{ y : \langle x \rangle = \langle y \rangle \}$. A graph is called integral if all its eigenvalues are integers. It is known that a Cayley graph is integral if and only if its connection set can be express as union of the sets $[x] $. In this paper, we determine an algebraic formula for eigenvalues of the integral Cayley graph when the connection set is $ [x]$. This formula involves an analogue of M$\ddot{\text{o}}$bius function. |
| title | A formula for eigenvalues of integral Cayley graphs over abelian groups |
| topic | Combinatorics 05C50, 20C15 |
| url | https://arxiv.org/abs/2411.06386 |