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Simple eigenvalues of cubic vertex-transitive graphs
If is an eigenvector for eigenvalue of a graph and
is an automorphism of , then is also an eigenvector for
. 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.Comment: 22 p
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