Geodesic
Niche Hypergraphs of Products of Digraphs
Discussiones Mathematicae. Graph Theory, Tome 40 (2020) no. 1, pp. 279-295

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If D = (V, A) is a digraph, its niche hypergraph N ℋ (D) = (V, ℰ ) has the edge set ℰ = { e ⊆ V | |e| ≤ 2 ∃ υ ∈ V : e = N_D^− (υ) 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 D_1 ∘ D_2 of digraphs D_1 and D_2, we investigate the relations between the niche hypergraphs of the factors D_1, D_2 and the niche hypergraph of their product D_1 ∘ D_2.
Keywords: niche hypergraph, product of digraphs, competition hypergraph 
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Sonntag, Martin; Teichert, Hanns-Martin. Niche Hypergraphs of Products of Digraphs. Discussiones Mathematicae. Graph Theory, Tome 40 (2020) no. 1, pp. 279-295. http://geodesic.mathdoc.fr/item/DMGT_2020_40_1_a18/