Zero divisor graphs of semigroups.
type: Item
instance of: scholarly article
title: Zero divisor graphs of semigroups.
zbMATH Open document ID: 1077.20069
author: Lisa DeMeyer
author: Frank R. DeMeyer
published in: Journal of Algebra
publication date: 2005-04-07T00:00:00Z
review text: Let \(S\) be a commutative semigroup with \(0\). A simple graph \(G\) whose vertices are the nonzero zero divisors of \(S\) with two distinct vertices joined by an edge in case when their product in \(S\) is \(0\) is called the zero divisor graph of \(S\). In the paper some characterizations of graphs to be zero divisor graphs of a semigroup are given. An association with \(S\) of a simplicial complex \(K(S)\) with \(S\), where a simplex is a subset \(A\) of \(S-\{0\}\) with the property that \(x,y\in A\) with \(x\neq y\) implies \(xy=0\) is introduced to give some interesting examples of zero divisor graphs, such as a graph \(G\) with the property that every edge in \(G\) is the edge of a triangle and \(G\) is the zero divisor graph of a semilattice but not the zero divisor graph for any nilpotent semigroup.
reviewed by: Vladimir Fleischer
Mathematics Subject Classification ID: 20M14
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 2153359
zbMATH Keywords: zero divisor graphs
zbMATH Keywords: simplicial complexes
zbMATH Keywords: nilpotent semigroups
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2004.08.028
OpenAlex ID: W2091909120
cites work: The zero-divisor graph of a commutative ring
cites work: Coloring of commutative rings
cites work: Q3848243
cites work: The zero-divisor graph of a commutative semigroup
cites work: CYCLES AND SYMMETRIES OF ZERO-DIVISORS
cites work: Q3827224
DOI: 10.1016/J.JALGEBRA.2004.08.028
description: scientific article; zbMATH DE number 2153359