Acyclic domination
type: Item
instance of: scholarly article
title: Acyclic domination
zbMATH Open document ID: 0961.05052
DOI: 10.1016/S0012-365X(00)00012-1
published in: Discrete Mathematics
publication date: 2000-09-14T00:00:00Z
review text: A subset \(S\) of the vertex set \(V(G)\) of a graph \(G\) is called dominating in \(G\), if each vertex of \(G\) either is in \(S\), or is adjacent to a vertex of \(S\). If, moreover, the subgraph \(\langle S\rangle\) of \(G\) induced by \(S\) contains no circuit, then \(S\) is an acyclic dominating set in \(G\). The minimum number of vertices of an acyclic dominating set in \(G\) is the acyclic domination number \(\gamma_a(G)\) of \(G\). In the paper this number is studied and compared with other numerical invariants of graphs concerning domination, mainly with the upper irredundance number \(\text{IR}(G)\) and the lower independence number \(\text{ir}(G)\).
reviewed by: Bohdan Zelinka
Mathematics Subject Classification ID: 05C60
Mathematics Subject Classification ID: 05C35
zbMATH DE Number: 1506824
zbMATH Keywords: acyclic dominating set
zbMATH Keywords: acyclic domination number
zbMATH Keywords: irredundance number
author: Sandra M. Hedetniemi
author: Stephen T. Hedetniemi
author: Douglas F. Rall
MaRDI profile type: Publication
full work available at URL: s0012-365x(00)00012-1
OpenAlex ID: W2914780524
description: scientific article; zbMATH DE number 1506824