Congruences and subdirect representations of graphs
<p class="p1">A basic tool in universal algebra is that of a congruence. It has been shown that congruences can be defined<span class="Apple-converted-space"> </span>for graphs with properties similar to their universal algebraic counterparts. In particular, a...
Main Author: | |
---|---|
Format: | Article |
Language: | English |
Published: |
Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia
2020-04-01
|
Series: | Electronic Journal of Graph Theory and Applications |
Subjects: | |
Online Access: | https://www.ejgta.org/index.php/ejgta/article/view/846 |
id |
doaj-62471276b92e4d53894c4f1ebca79cf4 |
---|---|
record_format |
Article |
spelling |
doaj-62471276b92e4d53894c4f1ebca79cf42021-03-11T01:13:06ZengIndonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), IndonesiaElectronic Journal of Graph Theory and Applications2338-22872020-04-018112313210.5614/ejgta.2020.8.1.9170Congruences and subdirect representations of graphsStefan Veldsman0Department of Mathematics, Nelson Mandela University, Port Elizabeth, South Africa<p class="p1">A basic tool in universal algebra is that of a congruence. It has been shown that congruences can be defined<span class="Apple-converted-space"> </span>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</p>https://www.ejgta.org/index.php/ejgta/article/view/846congruence on a graph, quotient graph, subdirect product of graphs, subdirectly irreducible graph, birkhoff's theorem |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Stefan Veldsman |
spellingShingle |
Stefan Veldsman Congruences and subdirect representations of graphs Electronic Journal of Graph Theory and Applications congruence on a graph, quotient graph, subdirect product of graphs, subdirectly irreducible graph, birkhoff's theorem |
author_facet |
Stefan Veldsman |
author_sort |
Stefan Veldsman |
title |
Congruences and subdirect representations of graphs |
title_short |
Congruences and subdirect representations of graphs |
title_full |
Congruences and subdirect representations of graphs |
title_fullStr |
Congruences and subdirect representations of graphs |
title_full_unstemmed |
Congruences and subdirect representations of graphs |
title_sort |
congruences and subdirect representations of graphs |
publisher |
Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia |
series |
Electronic Journal of Graph Theory and Applications |
issn |
2338-2287 |
publishDate |
2020-04-01 |
description |
<p class="p1">A basic tool in universal algebra is that of a congruence. It has been shown that congruences can be defined<span class="Apple-converted-space"> </span>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</p> |
topic |
congruence on a graph, quotient graph, subdirect product of graphs, subdirectly irreducible graph, birkhoff's theorem |
url |
https://www.ejgta.org/index.php/ejgta/article/view/846 |
work_keys_str_mv |
AT stefanveldsman congruencesandsubdirectrepresentationsofgraphs |
_version_ |
1714790744082874368 |