Congruences and Hoehnke Radicals on Graphs

Abstract

We 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).

Keywords

• congruences and quotients of graphs
• hoehnke radicals of graphs
• connectednesses and disconnectednesses of graphs
• kurosh-amitsur radicals of graphs
• subdirect representations of graphs
• 05c25
• 05c76
• 16n80
• 08a30