Product of digraphs and their competition graphs
Martin Sonntag, Hanns‐Martin Teichert · Discussiones Mathematicae Graph Theory · 2015
If D = (V, A) is a digraph, its competition graph (with loops) CG l (D) has the vertex set V and {u, v} V is an edge of CG l (D) if and only if there is a vertex w V such that (u, w), (v, w) A. In CG l (D), loops {v} are allowed only if v is the only predecessor of a certain vertex w V . For several products D 1 D 2 of digraphs D 1 and D 2 , we investigate the relations between the competition graphs of the factors D 1 , D 2 and the competition graph of their product D 1 D 2 .