Broere, IzakImrich, WilfriedKalinowski, RafalPilśniak, Monika2019-02-062019-08Broere, I., Imrich, W., Kalinowski, R. et al. 2019, 'Asymmetric colorings of products of graphs and digraphs', Discrete Applied Mathematics, vol. 266, pp. 56-64.0166-218X (print)1872-6771 (online)10.1016/j.dam.2018.12.023http://hdl.handle.net/2263/68412We 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.en© 2019 Elsevier B.V. All rights reserved. Notice : this is the author’s version of a work that was accepted for publication in Discrete Applied Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. A definitive version was subsequently published in Discrete Applied Mathematics, vol. 266, pp. 56-64, 2019. doi : 10.1016/j.dam.2018.12.023.Asymmetric coloringsAutomorphismsStrong productsDigraphsVertex coloringColoringDirected graphsGraphic methodsSet theoryCartesian products of graphsDirect products of graphsPrime factorizationProducts of graphsGraph theoryGraphsPostprint Article