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

Abstract

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