Graphs with regular monoids
type: Item
instance of: scholarly article
title: Graphs with regular monoids
zbMATH Open document ID: 1015.05031
DOI: 10.1016/S0012-365X(02)00625-8
author: Weimin Li
published in: Discrete Mathematics
publication date: 2003-05-25T00:00:00Z
review text: The author proves that the endomorphism monoid of \(\overline{C_n}\) \((n\geq 3)\) is regular where \(\overline{C_n}\) denotes the complement graph of a undirected cycle of \(n\) vertices. It is noted that \(\text{End}(\overline{C_6})\) is not an orthodox monoid. Moreover \(|\text{End}(\overline{C_{2m+1}})|= 4m +2\), \(|\text{End}(\overline{C_{2m}})|= 4(m+m!)\), and \(\text{End}(G)\) is a regular monoid iff \(\text{End}(G+K_n)\) is regular, \(n\geq 1\). In addition the author characterizes regular \(\text{End}(T_1+T_2)\) where \(T_1,T_2\) are trees, using known results on regularity of \(\text{End}(T)\), \(T\) a tree.
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 20M17
zbMATH DE Number: 1915538
zbMATH Keywords: monoid
zbMATH Keywords: regular endomorphism
zbMATH Keywords: tree
reviewed by: Ulrich Knauer
MaRDI profile type: Publication
full work available at URL: s0012-365x(02)00625-8
OpenAlex ID: W1969867831
description: scientific article; zbMATH DE number 1915538