On Self-Complementary Vertex-Transitive Graphs of Order a Product of Distinct Primes

Abstract

We show that a self-complementary vertex-transitive graph of order \(pq\), where \(p\) and \(q\) are distinct primes, is isomorphic to a circulant graph of order \(pq\). We will also show that if \(\Gamma\) is a self-complementary Cayley graph of the nonabelian group \(G\) of order \(pq\), then \(\Gamma\) and the complement of \(\Gamma\) are not isomorphic by a group automorphism of \(G\).