Constructions of Self-complementary Circulants with No Multiplicative Isomorphisms

The main topic of the paper is the question of the existence of self-complementary Cayley graphs Cay(G, S) with the property Sσ ≠ = G# \ S for all σ ∈ Aut(G). We answer this question in the positive by constructing an infinite family of self-complementary circulants with this property. Moreover, we obtain a complete classification of primes p for which there exist self-complementary circulants of order p2with this property.