A note on graphs which have upper irredundance equal to independence
type: Item
instance of: scholarly article
title: A note on graphs which have upper irredundance equal to independence
zbMATH Open document ID: 0784.05036
DOI: 10.1016/0166-218X(93)90224-C
author: Kenneth Peters
author: Michael Jacobson
published in: Discrete Applied Mathematics
publication date: 1994-03-20T00:00:00Z
review text: A subset \(D\) of the vertex set \(V(G)\) of a graph \(G\) is called independent, if no two vertices of \(D\) are adjacent in \(G\). A set \(I\subseteq V(G)\) is called irredundant, if for each \(x\in I\) either \(x\) is isolated, or there exists \(y\in V(G)-I\) adjacent to \(x\) and to no other vertex of \(I\). The greatest number of vertices of an independent (or irredundant) set in \(G\) is called the independence number \(\beta(G)\) (or upper irredundance number \(\text{IR}(G)\) respectively) of the graph \(G\). If \(\text{IR}(H)=\beta(H)\) for all induced subgraphs \(H\) of \(G\), then \(G\) is called irredundant perfect. These graphs are characterized. Some further results are presented concerning the upper domination number.
Mathematics Subject Classification ID: 05C35
Mathematics Subject Classification ID: 05C99
zbMATH DE Number: 428105
zbMATH Keywords: independence number
zbMATH Keywords: irredundance number
zbMATH Keywords: upper domination number
reviewed by: Bohdan Zelinka
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 428105