DESIGNS ARISING FROM PRODUCTS OF HYPERGRAPHS OF CYCLES

DESIGNS ARISING FROM PRODUCTS OF HYPERGRAPHS OF CYCLES

M. I. Huilgol, S. Asok

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Abstract

In this paper, we have considered many standard graph products viz. cartesian product, direct product, strong product and lexicographic product, and extended these graph products to hypergraphs which are natural generalizations of ususal graphs where edges may consist of more than two vertices. We have constructed a hypergraph of a graph by considering hyperedges as closed neighbourhood of each vertex in the graph. As the product of any two hypergraphs is again a hypergraph, we have obtained designs arising from products of hypergraphs where blocks are hyperedges of a hypergraph obtained by taking standard products of hypergraphs of cycles.

Keywords

PBIB-designs, Hypergraphs, Cartesian product, Direct product, Strong product, Lexicographic product.