Congruences and subdirect representations of graphs

Stefan Veldsman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


A basic tool in universal algebra is that of a congruence. It has been shown that congruences can be defined for graphs with properties similar to their universal algebraic counterparts. In particular, a subdirect product of graphs and hence also a subdirectly irreducible graph, can be expressed in terms of graph congruences. Here the subdirectly irreducible graphs are determined explicitly. Using congruences, a graph theoretic version of the well-known Birkhoff Theorem from universal algebra is given. This shows that any non-trivial graph is a subdirect product of subdirectly irreducible graphs.

Original languageEnglish
Pages (from-to)123-132
Number of pages10
JournalElectronic Journal of Graph Theory and Applications
Issue number1
Publication statusPublished - 2020
Externally publishedYes


  • Birkhoff's theorem
  • Congruence on a graph
  • Quotient graph
  • Subdirect product of graphs
  • Subdirectly irreducible graph

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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