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Disproof of a Conjecture in the Domination Theory

✍ Scribed by I. E. Zverovich; V. E. Zverovich

Publisher
Springer Japan
Year
1994
Tongue
English
Weight
227 KB
Volume
10
Category
Article
ISSN
0911-0119

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A dominating set D of a graph G is a least dominating set (I.d.s) if y((D)) < 2~((D~)) for any dominating set D1 (7 denotes domination number). The least domination number ~ ~ (G) of G is the minimum cardinality of a 1.d.s. We prove a conjecture of Sampathkumar (1990) that Vl ~< 3p/5 for any connect

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## Abstract The game domination number of a (simple, undirected) graph is defined by the following game. Two players, \documentclass{article}\usepackage{amssymb}\usepackage{amsbsy}\usepackage[mathscr]{euscript}\footskip=0pc\pagestyle{empty}\begin{document}${\mathcal{A}}$\end{document} and \docume