-partite self-complementary and almost self-complementary -uniform hypergraphs. Issue 1 (2nd January 2020) - Kamble, L.N.; Deshpande, C.M.; Athawale, B.P.
Abstract: A hypergraph H is said to be r -partite r -uniform if its vertex set V can be partitioned into non-empty sets V 1, V 2, . . ., V r so that every edge in the edge set E ( H ), consists of precisely one vertex from each set V i, i = 1, 2, …, r . It is denoted as H r ( V 1, V 2, …, V r ) or H ( n 1, n 2, …, n r ) r if | V i | = n i for i = 1, 2, … r . In this paper we define r -partite self-complementary and almost self-complementary r -uniform hypergraph. We prove that, there exists an r -partite self-complementary r -uniform hypergraph H r ( V 1, V 2, …, V r ) where | V i | = n i for i = 1, 2, …, r if and only if at least one of n 1, n 2, …, n r is even. And we prove that, there exists an r -pasc H r ( V 1, V 2, …, V r ) where | V i | = n i for i = 1, 2, …, r if and only if n 1, n 2, …, n r are odd. Further, we analyze the cycle structure of complementing permutations of r -partite self-complementary r -uniform hypergraphs and r -partite almost self-complementary r -uniform hypergraphs.