A Classification of DCI(CI)-Subsets for Cyclic Group of Odd Prime Power Order

Abstract

Let Zn be a cyclic group of order n and C(Zn, S) the circulant digraph of Zn with respect to S⊆Zn\{o}. S is called a DCI-subset of Zn if, for any circulant digraph C(Zn, T), C(Zn, S)≅C(Zn, T) implies that S and T are conjugate in Aut(Zn), the automorphism group of Zn. In this paper, we give a complete classification for DCI-subsets of Zn in the case of n=pa, where p is an odd prime.