The endomorphism monoid of \(\overline{P_n}\).
type: Item
instance of: scholarly article
title: The endomorphism monoid of \(\overline{P_n}\).
zbMATH Open document ID: 1151.20050
published in: European Journal of Combinatorics
publication date: 2008-05-29T00:00:00Z
review text: Let \(\overline{P_n}\) be the complement of the path \(P_n\) with \(n\) vertices (all graphs are finite undirected without loops and multiple edges). It is proved that the endomorphism monoid of \(\overline{P_n}\) is orthodox. The number of elements in \(\text{End}(\overline{P_n})\) and the endomorphism spectrum, i.e., the number of endomorphisms of a particular type (half-strong, locally strong, quasi-strong, strong endomorphisms and automorphisms) are also found.
reviewed by: Jaak Henno
Mathematics Subject Classification ID: 20M20
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 08A35
zbMATH DE Number: 5280758
zbMATH Keywords: endomorphism monoids
zbMATH Keywords: graphs
zbMATH Keywords: path complements
zbMATH Keywords: orthodox semigroups
author: Hailong Hou
author: Yanfeng Luo
author: Zhi-Mi Cheng
MaRDI profile type: Publication
full work available at URL: j.ejc.2007.06.026
OpenAlex ID: W2063453783
cites work: Q4846425
cites work: Endomorphism spectra of graphs
cites work: On End-regular graphs
cites work: Endomorphism-regularity of split graphs
cites work: A regular endomorphism of a graph and its inverses
cites work: Problems raised at the Problem Session of the Colloquium on Semigroups in Szeged, August 1987
cites work: Q4484922
cites work: Graphs with a regular endomorphism monoid
DOI: 10.1016/J.EJC.2007.06.026
description: scientific article; zbMATH DE number 5280758