The monoid of strong endomorphisms of a graph
type: Item
instance of: scholarly article
title: The monoid of strong endomorphisms of a graph
zbMATH Open document ID: 0808.20055
DOI: 10.1007/BF02573480
author: Weimin Li
published in: Semigroup Forum
publication date: 1995-03-16T00:00:00Z
full work available at URL: https://eudml.org/doc/135343
review text: The author investigates strong endomorphisms of finite undirected graphs without loops and multiple edges. A strong endomorphism is a mapping on the vertex set which preserves and reflects edges (i.e. the preimage of an edge is an edge). The author studies Green's \(\mathcal R\) and \(\mathcal L\) classes of the monoids of strong endomorphisms. He describes idempotents in these classes and all inverses to any strong endomorphism taking into account that the monoid of strong endomorphisms is always regular, i.e. inverses in this sense do exist. He also gives formulas for the number of idempotents and inverses.
Mathematics Subject Classification ID: 20M20
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 20M15
Mathematics Subject Classification ID: 08A30
Mathematics Subject Classification ID: 20M17
zbMATH DE Number: 638349
zbMATH Keywords: undirected graphs
zbMATH Keywords: monoid of strong endomorphisms
zbMATH Keywords: idempotents
zbMATH Keywords: inverses
reviewed by: Ulrich Knauer
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: Green's relations on the strong endomorphism monoid of a graph
cites work: Regular D -Classes in Semigroups
description: scientific article; zbMATH DE number 638349