image-decompositions of some regular graphs Original Research Article

In this paper, for any prime image, we consider image-decompositions of image and image and also image-factorizations of image, where image and image denote the tensor product and wreath product of graphs, respectively, (image is isomorphic to the complete m-partite graph in which each partite set has exactly n vertices). It has been proved that for image, image-decomposes image if and only if (1) either m or n is odd and (2) image. Further, it is shown that for image, image-decomposes image if and only if (1) image is even and (2) image. Except possibly for some valid pairs of integers m and image, the necessary conditions for the existence of image-factorization of image are proved to be sufficient.