Simple eigenvalues of vertextransitive graphs
Simple eigenvalues of vertextransitive 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 vertextransitive graph with all eigenvalues simple is K_2 and it is wellknown that a kregular vertextransitive graph will have at most k+1 simple eigenvalues. We will look at structural properties of vertextransitive graphs with many simple eigenvalues.