For two graphs G and H their wreath product\documentclass[12pt]{minimal}
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\begin{document}$${G \otimes H}$$\end{document} has the vertex set \documentclass[12pt]{minimal}
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\begin{document}$${V(G) \times V(H)}$$\end{document} in which two vertices (g1, h1) and (g2, h2) are adjacent whenever \documentclass[12pt]{minimal}
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\begin{document}$${g_{1}g_{2} \in E(G)}$$\end{document} or g1 = g2 and \documentclass[12pt]{minimal}
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\begin{document}$${h_{1}h_{2} \in E(H)}$$\end{document} . Clearly \documentclass[12pt]{minimal}
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\begin{document}$${K_{m} \otimes I_{n}}$$\end{document} , where In is an independent set on n vertices, is isomorphic to the complete m-partite graph in which each partite set has exactly n vertices. A subgraph of the complete multipartite graph \documentclass[12pt]{minimal}
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\begin{document}$${K_m \otimes I_n}$$\end{document} containing vertices of all but one partite set is called partial factor. An H-frame of \documentclass[12pt]{minimal}
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\begin{document}$${K_m \otimes I_n}$$\end{document} is a decomposition of \documentclass[12pt]{minimal}
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\begin{document}$${K_m \otimes I_n}$$\end{document} into partial factors such that each component of it is isomorphic to H. In this paper, we investigate C2k-frames of \documentclass[12pt]{minimal}
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\begin{document}$${(K_m \otimes I_n)(\lambda)}$$\end{document} , and give some necessary or sufficient conditions for such a frame to exist. In particular, we give a complete solution for the existence of a C4p-frame of \documentclass[12pt]{minimal}
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\begin{document}$${(K_m \otimes I_n)(\lambda)}$$\end{document} , where p is a prime, as follows: For an integer m ≥ 3 and a prime p, there exists a C4p-frame of \documentclass[12pt]{minimal}
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\begin{document}$${(K_m \otimes I_n)(\lambda)}$$\end{document} if and only if \documentclass[12pt]{minimal}
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\begin{document}$${(m-1)n \equiv 0 ({\rm {mod}} {4p})}$$\end{document} and at least one of m, n must be even, when λ is odd.
