Simple eigenvalues of vertex-transitive graphs

Krystal Guo , Simon Fraser University
Fine Hall 224

A simple eigenvalue of a graph is an eigenvalue of the adjacency matrix with multiplicity 1. It has been observed that graphs having many simple eigenvalues tend to have small automorphism groups. The only vertex-transitive graph with all eigenvalues simple is K_2 and it is well-known that a k-regular vertex-transitive graph will have at most k+1 simple eigenvalues. We will look at structural properties of vertex-transitive graphs with many simple eigenvalues.