Paley graphs represent a useful class of graphs with interesting properties. Classically, for each prime number p, we can construct the corresponding Paley graph using quadratic and non-quadratic residues modulo p. In this talk, we introduce the generalized Paley graphs. These are graphs that are associated with a general quadratic character. We will then provide some of their basic properties. In particular, we describe their spectrum explicitly and then utilize them to construct some new families of Ramanujan graphs. Time permitting, we will provide an effective upper bound for the Cheeger number of these generalized Paley graphs.

Zoom Meeting ID: 860 5058 4049

Passcode: 901444