Isomorphic factorization of the complete graph into Cayley digraphs

Abstract

AbstractLet Zp denote the cyclic group of order p where p is a prime number. Let X = X(Zp, H) denote the Cayley digraph of Zp with respect to the symbol H. We obtain a necessary and sufficient condition on H so that the complete graph on p vertices can be edge‐partitioned into three copies of Cayley digraphs of the same group Zp each isomorphic to X. Based on this condition on H, we then enumerate all such Cayley graphs and digraphs. © 2006 Wiley Periodicals, Inc. J Graph Theory 52: 243–256, 2006