\(H\)-forming sets in graphs
type: Item
instance of: scholarly article
title: \(H\)-forming sets in graphs
zbMATH Open document ID: 1017.05082
DOI: 10.1016/S0012-365X(02)00496-X
author: Teresa W. Haynes
author: Stephen T. Hedetniemi
author: Michael A. Henning
author: Peter Slater
published in: Discrete Mathematics
publication date: 2003-04-28T00:00:00Z
review text: The \(H\)-forming number of a graph \(G\) is one of the modern variants of numbers concerning domination in graphs. Let \(G\) and \(H\) be graphs. An \(H\)-forming set of \(G\) is a set \(S\subseteq V(G)\) such that for each \(v\in V(G)-S\) there exists a subset \(R\) of \(S\) with \(|R|=|V(H)|-1\) and such that the subgraph induced by \(R\cup\{v\}\) contains \(H\) as subgraph. The minimum number of vertices of an \(H\)-forming set in \(G\) is the \(H\)-forming number \(\gamma_{(H)}(G)\) of \(G\). In this paper the \(H\)-forming number is studied and compared with the domination number and the total domination number. Special attention is devoted to the case that \(H\) is a path of length 2.
reviewed by: Bohdan Zelinka
Mathematics Subject Classification ID: 05C69
zbMATH DE Number: 1901897
zbMATH Keywords: total domination
zbMATH Keywords: independence
zbMATH Keywords: \(H\)-forming number
MaRDI profile type: Publication
full work available at URL: s0012-365x(02)00496-x
OpenAlex ID: W2091316897
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description: scientific article; zbMATH DE number 1901897