On the Paley graph of a quadratic character

Tóm tắt báo cáo

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.  Time permitting, we will provide an effective upper bound for the Cheeger number of these generalized Paley graphs.