UVictoria Discrete Math Seminar: Maxwell Levit

Algebraic graph theory begins by associating a matrix to a graph and asking how the eigenvalues of the former relate to the structure of the latter. In the past fifteen or so years, horizons have broadened to include variants of graphs (such as signed graphs or directed graphs) which require variants of adjacency matrices such as signed or Hermitian adjacency matrices. I will focus on the topic of characterizing the graphs whose associated matrices have at most three distinct eigenvalues. I will discuss old results in the undirected and signed graph case and then present some new results for oriented graphs.

Based on joint work with S. Akbari, J. Aloni, B. Mohar and S. Xia.