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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Stefan Veldsman
Department of Mathematics, Nelson Mandela University, Port Elizabeth, South Africa
Electrical & Electronics Engineering

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Congruences and subdirect representations of graphs Stefan Veldsman
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 8, No 1 (2020): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2020.8.1.9

Abstract

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
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