Broere, IzakHeidema, JohannesVeldsman, Stefan2020-10-292020-10-292020Broere, I., Heidema, J. & Veldsman, S. 2020, 'Congruences and Hoehnke radicals on graphs', Discussiones Mathematicae Graph Theory, vol. 40, no. 4, pp. 1067-1084.1234-3099 (print)2083-5892 (online)10.7151/dmgt.2166http://hdl.handle.net/2263/76662We motivate, introduce, and study radicals on classes of graphs. This concept, and the theory which is developed, imitates the original notion of a Hoehnke radical in universal algebra using congruences. It is shown how this approach ties in with the existing theory of connectednesses and disconnectednesses (= Kurosh-Amitsur radical theory).en© Authors. This article is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.Kurosh-Amitsur radicals of graphsSubdirect representations of graphsCongruences of graphsQuotients of graphsConnectednesses of graphsDisconnectednesses of graphsArticle