Abstract

A kite K is a graph which can be obtained by joining an edge to any vertex of K 3 . A kite with edge set { a b , b c , c a , c d } can be denoted as ( a , b , c ; c d ) . If every vertex of a kite in the decomposition lies in different partite sets, then we say that a kite decomposition of a multipartite graph is a gregarious kite decomposition. In this manuscript, it is shown that there exists a decomposition of ( K m ⊗ ¯¯¯¯¯ K n ) × ( K r ⊗ ¯¯¯¯¯ K s ) into gregarious kites if and only if n 2 s 2 m ( m − 1 ) r ( r − 1 ) ≡ 0 ( mod 8 ) , where ⊗ and × denote the wreath product and tensor product of graphs respectively. We denote a gregarious kite decomposition as G K -decomposition.

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