Diametral designs arising from hypergraph of some classes of diameter 3 distance regular graphs

Abstract

Hypergraph is a graph H = (V, E) where V is the set of vertices and E is the set containing subsets of elements from set V . The elements of set E are called hyperedges and these need not always be of order 2 as in the case of graphs. In this paper, we have considered 3 classes of distance regular graphs (DRGs) of diameter 3 namely, crown graph, Johnson graph and Hamming graph. We have considered hypergraph models of these graphs and obtained the parameters of diametral designs arising from them. We have also obtained a condition when hypergraph H1 of DRGs with diameter 3 forms a strongly regular graph with parameters (n, n − 2, n − 4, n − 2).