Products of digraphs and their competition graphs

Abstract

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 ο 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 ο D2.