The diameter of total domination vertex critical graphs
type: Item
instance of: scholarly article
title: The diameter of total domination vertex critical graphs
zbMATH Open document ID: 1055.05113
author: Teresa W. Haynes
author: Michael A. Henning
author: Wayne Goddard
author: Lucas van der Merwe
published in: Discrete Mathematics
publication date: 2004-11-22T00:00:00Z
review text: A graph \(G\) with total domination number \(\gamma_t(G)=k\) is called \(k\)-\(\gamma_t\)-critical if \(\gamma_t(G-v)<k\) for all vertices \(v\) for which \(G-v\) contains no isolated vertex. The authors characterize connected \(k\)-\(\gamma_t\)-critical graphs having at least one endvertex and derive a sharp upper bound on their diameter. Furthermore, they prove that the maximum possible diameter of connected \(k\)-\(\gamma_t\)-critical graphs in general lies between \(5k/3-O(1)\) and \(2k-3\) and determine the exact values for \(k\leq 8\).
reviewed by: Dieter Rautenbach
Mathematics Subject Classification ID: 05C69
zbMATH DE Number: 2117318
zbMATH Keywords: total domination
zbMATH Keywords: vertex critical
zbMATH Keywords: diameter
MaRDI profile type: Publication
full work available at URL: j.disc.2004.05.010
OpenAlex ID: W1997029072
cites work: Vertex domination-critical graphs
cites work: Total domination in graphs
cites work: The diameter of domination k‐critical graphs
cites work: Vertex domination‐critical graphs
cites work: Q4443245
cites work: Q4368728
cites work: Graphs with large total domination number
cites work: Critical concepts in domination
cites work: Domination critical graphs
cites work: Q4378638
cites work: Hamiltonian properties of domination-critical graphs
DOI: 10.1016/J.DISC.2004.05.010
description: scientific article; zbMATH DE number 2117318