Simple eigenvalues of cubic vertex-transitive graphs
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866909394943344640 |
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| author | Guo, Krystal Mohar, Bojan |
| author_facet | Guo, Krystal Mohar, Bojan |
| contents | If $v$ is an eigenvector for eigenvalue $λ$ of a graph $X$ and $α$ is an automorphism of $X$, then $α(v)$ is also an eigenvector for $λ$. Thus it is rather exceptional for an eigenvalue of a vertex-transitive graph to be simple. We study cubic vertex-transitive graphs with a non-trivial simple eigenvalue, and discover remarkable connections to arc-transitivity, regular maps and Chebyshev polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2002_05694 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Simple eigenvalues of cubic vertex-transitive graphs Guo, Krystal Mohar, Bojan Combinatorics 05C50, 05C25 If $v$ is an eigenvector for eigenvalue $λ$ of a graph $X$ and $α$ is an automorphism of $X$, then $α(v)$ is also an eigenvector for $λ$. Thus it is rather exceptional for an eigenvalue of a vertex-transitive graph to be simple. We study cubic vertex-transitive graphs with a non-trivial simple eigenvalue, and discover remarkable connections to arc-transitivity, regular maps and Chebyshev polynomials. |
| title | Simple eigenvalues of cubic vertex-transitive graphs |
| topic | Combinatorics 05C50, 05C25 |
| url | https://arxiv.org/abs/2002.05694 |