A class of graphs with a few well-covered members
type: Item
instance of: scholarly article
title: A class of graphs with a few well-covered members
zbMATH Open document ID: 1466.13019
author: T. Ashitha
author: T. Asir
author: M. R. Pournaki
published in: Expositiones Mathematicae
publication date: 2021-07-15T00:00:00Z
review text: Several graphs are associated with commutative rings and they are used as combinatorial tools to study algebraic properties of commutative rings. Let \(R\) be a commutative ring with identity \(1\neq 0.\) The total graph \(T(R)\) of \(R\) is the simple undirected graph with vertex set \(R\) and two distinct vertices \(x\) and \(y\) are adjacent in \(T(R)\) whenever \(x+y\) is a zerodivisor of \(R.\) A graph is said to be well covered if its all maximal independent sets have the same number of vertices. In this paper, authors characterized all finite commutative rings \(R\) for which the total graph \(T(R)\) is well covered. In fact it is proved that \(T (R)\) is well-covered if and only if either \(R\) is local or \(2(=1+1)\) is a zero-divisor of \(R.\)
reviewed by: T. Tamizh Chelvam
Mathematics Subject Classification ID: 13M99
Mathematics Subject Classification ID: 13A70
Mathematics Subject Classification ID: 05C69
zbMATH DE Number: 7371953
zbMATH Keywords: finite ring
zbMATH Keywords: total graph
zbMATH Keywords: maximal independent set
zbMATH Keywords: well-covered graph
MaRDI profile type: Publication
full work available at URL: j.exmath.2021.03.001
OpenAlex ID: W3139307083
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DOI: 10.1016/J.EXMATH.2021.03.001
description: scientific article; zbMATH DE number 7371953