Algebraic Graph Theory Seminar - Krystal Guo

Title: Simple eigenvalues of graph

Abstract:

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.