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1 results

Simple eigenvalues of cubic vertex-transitive graphs
Part of
- Algebraic combinatorics
- Graph theory
Krystal Guo, Bojan Mohar
Journal:

Canadian Journal of Mathematics / Volume 76 / Issue 5 / October 2024

Published online by Cambridge University Press:

10 August 2023, pp. 1496-1519

Print publication:

October 2024
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If ${\mathbf v} \in {\mathbb R}^{V(X)}$ is an eigenvector for eigenvalue $\lambda $ of a graph X and $\alpha $ is an automorphism of X, then $\alpha ({\mathbf v})$ is also an eigenvector for $\lambda $. Thus, it is rather exceptional for an eigenvalue of a vertex-transitive graph to have multiplicity one. We study cubic vertex-transitive graphs with a nontrivial simple eigenvalue, and discover remarkable connections to arc-transitivity, regular maps, and number theory.