-Factorization of the symmetric digraph of wreath product of graphs

In this paper, we show that the necessary and sufficient condition for the existence of an e Sk-factorization of (Cm ◦ Kn)∗ is n ≡ 0 (mod k(k − 1)), for all m > 3. In fact, our result together with a result of Ushio gives a complete solution for the existence of an e Sk-factorization of (Cm ◦Kn)∗ for all m ≥ 3. Further, we have obtained some necessary or sufficient conditions for the existence of an e Sk-factorization of K ∗ n1,n2,...,nm , for all even k ≥ 4 and m > 3.