$\widetilde{S}_k$-Factorization of the symmetric digraph of wreath product of graphs

Abstract

In this paper, we show that the necessary and sufficient condition for the existence of an [Formula: see text]-factorization of [Formula: see text] 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 [Formula: see text]-factorization of [Formula: see text] for all m ≥ 3. Further, we have obtained some necessary or sufficient conditions for the existence of an [Formula: see text]-factorization of [Formula: see text], for all even k ≥ 4 and m > 3.