Algebraic Graph Theory Seminar - Olha Silina

Title: Graph covers with two new eigenvalues

Abstract:

I am going to talk about graph covers. If $Y$ is a cyclic cover of $X$, it turns out that $Y$ has the same spectrum as $X$ plus (possibly) some new eigenvalues. In the cases when $X$ is a complete or complete bipartite graph, while $Y$ only has two new eigenvalues compared to $X$, it can be shown that $Y$ is distance regular.