Niche Hypergraphs of Products of Digraphs - Sonntag Martin; Teichert Hanns-Martin (Discussiones Mathematicae Graph Theory, 2020)
If D = (V, A) is a digraph, its niche hypergraph Nℋ(D) = (V, ℰ) has the edge set ℰ={e⊆V||e|≥2∧∃ υ∈V:e=ND−(υ)∨e=ND+(υ)}{\cal E} = \{ {e \subseteq V| | e | \ge 2 \wedge \exists \, υ \in V:e = N_D^ - ( υ ) \vee e = N_D^ + ( 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 ◦ 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 ◦ D2.