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.
Broere, Izak; Pilsniak, Monika(University of Primorska, Slovenia , Society of Mathematicians, Physicists and Astronomers of Slovenia and the Institute of Mathematics, Physics and Mechanics in Ljubljana, 2017)
Rado constructed a (simple) denumerable graph R with the positive integers
as vertex set with the following edges: for given m and n with m < n, m is
adjacent to n if n has a 1 in the mth position of its binary expansion. ...
Rado constructed a (simple) denumerable graph R with the positive integers as vertex set
with the following edges: For given m and n with m < n, m is adjacent to n if n has a 1 in
the m'th position of its binary expansion. ...
