Algebraic Graph Theory Seminar - Sabrina Lato

Title: New Characterizations of Distance-Biregular Graphs

Abstract: Fiol, Garriga, and Yebra introduced the notion of pseudo-distance-regular vertices, and were able to use this notion to come up with a characterization of when a graph is distance-regular. Subsequently, Fiol and Garriga were able to use pseudo-distance-regular vertices and a bound on the excess of a vertex to come up with another characterization of distance-regular graphs. We will present an overview of their results, as well as recent extensions to distance-biregular graphs.