The cyclic groups with the m-DCI property

For a finite group G and a subset S of G which does not contain the identity of G, let Cay(G, S) denote the Cayley graph of G with respect to S. If, for all subsets S, T of G of size m, Cay(G,S) congruent to Cay(G, T) implies S-alpha = T for some alpha is an element of Aut(G), then G is said to have the m-DCI property. In this paper, a classification is presented of the cyclic groups with the m-DCI property, which is reasonably complete. (C) 1997 Academic Press Limited.