Bounds relating generalized domination parameters
type: Item
instance of: scholarly article
title: Bounds relating generalized domination parameters
zbMATH Open document ID: 0781.05031
DOI: 10.1016/0012-365X(93)90567-D
author: Michael A. Henning
author: H. C. Swart
published in: Discrete Mathematics
publication date: 1993-11-01T00:00:00Z
review text: The paper studies a generalization of the domination number of a graph. For any integer \(n\geq 2\) the vertices \(u\), \(v\) of a graph \(G\) are said to be \(K_ n\)-adjacent, if there is a subgraph of \(G\) isomorphic to the complete graph \(K_ n\) with \(n\) vertices and containing the vertices \(u\), \(v\). A subset \(D\) of the vertex set \(V(G)\) of \(G\) is called \(K_ n\)-dominating (or total \(K_ n\)-dominating), if for every \(x\in V(G)-D\) (or every \(x \in D\), respectively) there exists a vertex \(y\in D\) which is \(K_ n\)-adjacent to \(x\). The minimum number of vertices of a \(K_ n\)-dominating (or total \(K_ n\)-dominating) set in \(G\) is called the \(K_ n\)-domination number (or total \(K_ n\)-domination number) of \(G\) and denoted by \(\gamma_{K_ n}(G)\) (or \(\gamma^ t_{K_ n}(G)\), respectively). In the paper two inequalities for the sum \(\gamma_{K_ 3}(G)+\gamma^ t_{K_ 3}(G)\) are proved and it is conjectured that analogous inequalities hold for \(\gamma_{K_ n}(G)+\gamma^ t_{K_ n}(G)\) in general.
Mathematics Subject Classification ID: 05C35
zbMATH DE Number: 429137
zbMATH Keywords: generalized domination
zbMATH Keywords: \(K_ n\)-domination number
zbMATH Keywords: total \(K_ n\)- domination number
zbMATH Keywords: inequalities
reviewed by: Bohdan Zelinka
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 429137