The Cyclic Groups with them-DCI Property

For a finite groupGand a subsetSofGwhich does not contain the identity ofG,let Cay(G, S)denote the Cayley graph ofGwith respect toS.If, for all subsetsS, TofGof sizem,Cay(G, S)≅Cay(G, T)impliesSα=Tfor someα∈Aut(G), thenGis said to have them-DCI property. In this paper, a classification is presented of the cyclic groups with them-DCI property, which is reasonably complete.