Algebraic Graph Theory - Krystal Guo

Title: Strongly regular subconstituents of strongly regular graphs

Abstract: A graph is strongly regular if every vertex has valency k, every pair of adjacency vertices have a common neighbours and every pair of non-adjacent vertices have c common neighbours. We will consider strongly regular graphs where the set of vertices at distance 2 (or 1) from a given vertex is again strongly regular.  We will look at the local eigenvalues of a graph and spherical 3-designs.