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 S-sigma not equal G(#) \ S for all sigma is an element of 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 p(2) with this property. (C) 2001 Academic Press.