Niche hypergraphs of products of digraphs

If D = (V, A) is a digraph, its niche hypergraph NH(D) = (V, ϵ) has the edge set ϵ={e⊆V||e|≥2δ υϵV:e=ND-(υ). Niche hypergraphs generalize the well-known niche graphs and are closely related to competition hypergraphs as well as common enemy hypergraphs. For several products D₁ &omicron D₂ of digraphs D₁ and D₂, we investigate the relations between the niche hypergraphs of the factors D₁, D₂ and the niche hypergraph of their product D₁ &omicron D₂