Title: Cospectral Vertices and Isospectral Reductions
|Affiliation:||Brigham Young University|
|Zoom:||Contact Soffia Arnadottir|
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.