Evenly partite star factorization of symmetric digraph of wreath product of graphs

For any graph G, let G∗ be the symmetric digraph obtained from G by replacing every edge with a pair of symmetric arcs. In this paper, we show that the necessary and sufficient condition for the existence of an S¯k-factorization in (Cm∘K¯n)∗ is n≡0(modk(k−1)2), where k>3 is odd. In fact, our result deduces the result of Ushio on symmetric complete tripartite digraphs as a corollary. Further, a necessary condition and some sufficient conditions for the existence of an S¯k-factorization in Kn1,n2,…,nm∗ are obtained.