On the Paley graph of a quadratic character

Time: 9:30 - 11:00, Jan 11, 2023.

Venue: Room 612, A6, Institute of Mathematics, VAST

Abstract: 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 discuss generalized Paley graphs. These are graphs that are associated with a general quadratic character. We will provide some of their basic properties. In particular, we describe their spectrum explicitly and use them to construct some new families of Ramanujan graphs. We will also provide an effective upper bound for the Cheeger number of these generalized Paley graphs.