Geodesic
Simple eigenvalues of cubic vertex-transitive graphs
Canadian journal of mathematics, Tome 76 (2024) no. 5, pp. 1496-1519

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DOI

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.
DOI : 10.4153/S0008414X23000482
Mots-clés : Algebraic graph theory, graph eigenvalues, vertex-transitive graphs, graph embeddings 
Guo, Krystal; Mohar, Bojan. Simple eigenvalues of cubic vertex-transitive graphs. Canadian journal of mathematics, Tome 76 (2024) no. 5, pp. 1496-1519. doi: 10.4153/S0008414X23000482
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