Strongly cospectral vertices in normal Cayley graphs

Abstract

We prove an upper bound on the number of pairwise strongly cospectral vertices in a normal Cayley graph, in terms of the multiplicities of its eigenvalues. We use this to determine an explicit bound in Cayley graphs of Z2d and Z4d. We also provide some infinite families of Cayley graphs of Z2d with a set of four pairwise strongly cospectral vertices and show that such graphs exist in every dimension.