Simple eigenvalues of cubic vertex-transitive graphs

Fuente: arXiv
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Hauptverfasser: Guo, Krystal, Mohar, Bojan
Format: Preprint
Veröffentlicht: 2020
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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