Abstract
Abstract
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.
Publisher
Canadian Mathematical Society