Geodesic
Products Of Digraphs And Their Competition Graphs
Discussiones Mathematicae. Graph Theory, Tome 36 (2016) no. 1, pp. 43-58

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If D = (V, A) is a digraph, its competition graph (with loops) CGl(D) has the vertex set V and u, v ⊆ V is an edge of CGl(D) if and only if there is a vertex w ∈ V such that (u, w), (v, w) ∈ A. In CGl(D), loops v are allowed only if v is the only predecessor of a certain vertex w ∈ V. For several products D1 ⚬ D2 of digraphs D1 and D2, we investigate the relations between the competition graphs of the factors D1, D2 and the competition graph of their product D1 ⚬ D2.
Keywords: competition graph, product of digraphs 
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Sonntag, Martin; Teichert, Hanns-Martin. Products Of Digraphs And Their Competition Graphs. Discussiones Mathematicae. Graph Theory, Tome 36 (2016) no. 1, pp. 43-58. http://geodesic.mathdoc.fr/item/DMGT_2016_36_1_a3/