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On Paired and Double Domination in Graphs

A paired dominating set of a graph G is a dominating set of vertices whose induced subgraph has a perfect matching, and a double dominating set is a dominating set that dominates every vertex of G at least twice. First a necessary and sufficient condition is given for a double dominating set (respectively, paired dominating set) to be minimal in G. We show that for clawfree graphs, the paired domination number is less than or equal to the double domination number. Then bounds on the double and paired domination numbers are presented. Sums involving these parameters are also considered.

Identiferoai:union.ndltd.org:ETSU/oai:dc.etsu.edu:etsu-works-19671
Date01 May 2005
CreatorsChellali, Mustapha, Haynes, Teresa W.
PublisherDigital Commons @ East Tennessee State University
Source SetsEast Tennessee State University
Detected LanguageEnglish
Typetext
SourceETSU Faculty Works

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