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.
Original language | English |
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Pages (from-to) | 123-132 |
Number of pages | 10 |
Journal | Electronic Journal of Graph Theory and Applications |
Volume | 8 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2020 |
Externally published | Yes |
Keywords
- 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