Green's relations on the strong endomorphism monoid of a graph
type: Item
instance of: scholarly article
title: Green's relations on the strong endomorphism monoid of a graph
zbMATH Open document ID: 0791.20077
DOI: 10.1007/BF02573757
author: Weimin Li
published in: Semigroup Forum
publication date: 1993-12-20T00:00:00Z
full work available at URL: https://eudml.org/doc/135270
review text: An endomorphism of a graph is called strong if in addition to preserving edges it also reflects edges. The author describes inside the graph Green's relations \(\mathcal L\), \(\mathcal R\), \(\mathcal H\) and \(\mathcal D\) for pairs of strong graph endomorphisms. As a consequence the author proves that the monoid of strong endomorphisms \(S\text{ End}(G)\) is regular. The methods are used to construct \(u \in S \text{ End}(G)\) with \(uf = g\) for \(f,g \in S \text{ End}(G)\) with \((f,g) \in {\mathcal L}\). All graphs are finite and undirected.
reviewed by: Ulrich Knauer
Mathematics Subject Classification ID: 20M20
Mathematics Subject Classification ID: 20M30
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 20M15
Mathematics Subject Classification ID: 20M17
zbMATH DE Number: 436439
zbMATH Keywords: Green's relations
zbMATH Keywords: strong graph endomorphisms
zbMATH Keywords: monoid of strong endomorphisms
MaRDI profile type: Publication
cites work: On the structure of semigroups
cites work: Q5572939
cites work: Q4126563
cites work: Endomorphisms of graphs. I: The monoid of strong endomorphisms
cites work: Endomorphisms of graphs. II: Various unretractive graphs
cites work: Regular D -Classes in Semigroups
OpenAlex ID: W2042662395
description: scientific article; zbMATH DE number 436439