Asymmetric colorings of products of graphs and digraphs

Abstract

We extend results about asymmetric colorings of finite Cartesian products of graphs to strong and direct products of graphs and digraphs. On the way we shorten proofs for the existence of prime factorizations of finite digraphs and characterize the structure of the automorphism groups of strong and direct products. The paper ends with results on asymmetric colorings of Cartesian products of finite and infinite digraphs.