Hereditary Torsion Theories for Graphs

S. Veldsman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

Using congruences, a Hoehnke radical can be defined for graphs in the same way as for universal algebras. This leads in a natural way to the connectednesses and disconnectednesses (= radical and semisimple classes) of graphs. It thus makes sense to talk about ideal-hereditary Hoehnke radicals for graphs (= hereditary torsion theories). All such radicals for the category of undirected graphs which allow loops are explicitly determined. Moreover, in contrast to what is the case for the well-known algebraic categories, it is shown here that such radicals for graphs need not be Kurosh–Amitsur radicals.

Original languageEnglish
Pages (from-to)363-378
Number of pages16
JournalActa Mathematica Hungarica
Volume163
Issue number2
DOIs
Publication statusPublished - Apr 2021
Externally publishedYes

Keywords

  • connectedness and disconnectedness of graphs
  • graph congruence
  • Hoehnke radical
  • ideal-hereditary radical
  • Kurosh–Amitsur radical
  • torsion theory

ASJC Scopus subject areas

  • Mathematics(all)

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