Algebraic Graph Theory: Strongly cospectral vertices, Cayley graphs and other things

Talk by Soffia Arnadottir.

In this talk we will look at a connection between the number of pairwise strongly cospectral vertices in a translation graph (a Cayley graph of an abelian group) and the multiplicities of its eigenvalues. We will use this connection to give an upper bound on the number of pairwise strongly cospectral vertices in cubelike graphs.