Paley-type graphs of order a product of two distinct primes

Abstract

In this paper, we initiate the study of Paley-type graphs ГN modulo N = pq, where p, q are distinct primes of the form 4k + 1. It is shown that ГN is an edge-regular, symmetric, Eulerian and Hamiltonian graph. Also, the vertex connectivity, edge connectivity, diameter and girth of ГN are studied and their relationship with the forms of p and q are discussed. Moreover, we specify the forms of primes for which ГN is triangulated or trianglefree and provide some bounds (exact values in some particular cases) for the order of the automorphism group Aut(ГN) of the graph ГN, the chromatic number, the independence number, and the domination number of ГN.