Abstract
In this paper, a new concept of an optimal complete multipartite decomposition of type 1 (type 2) of a complete n-partite graph Qn is proposed and another new concept of a normal complete multipartite decomposition of Kn is introduced. It is showed that an optimal complete multipartite decomposition of type 1 of Kn is a normal complete multipartite decomposition. As for any complete multipartite decomposition of Kn, there is a derived complete multipartite decomposition for Qn. It is also showed that any optimal complete multipartite decomposition of type 1 of Qn is a derived decomposition of an optimal complete multipartite decomposition of type 1 of Kn. Besides, some structural properties of an optimal complete multipartite decomposition of type 1 of Kn are given.
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