Algebraic Graph Theory Seminar - Mark Kempton

Title: Cospectral Vertices and Isospectral Reductions

Abstract:

Understanding cospectral vertices in graphs is fundamental to understanding what the spectrum of the adjacency matrix can tell us about a graph.  Furthermore, cospectral vertices are necessary in constructions of graphs exhibiting perfect quantum state transfer.  I will talk about how to recognize cospectral vertices via a tool from network dynamics: the isospectral reduction of a graph.  I will explore possible ways of getting new constructions of cospectral vertices by looking at isospectral reductions.