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H-forming Sets in Graphs

For graphs G and H, a set S⊆V(G) is an H-forming set of G if for every v∈V(G)-S, there exists a subset R⊆S, where |R|=|V(H)|-1, such that the subgraph induced by R∪{v} contains H as a subgraph (not necessarily induced). The minimum cardinality of an H-forming set of G is the H-forming number γ {H}(G). The H-forming number of G is a generalization of the domination number γ(G) because γ(G)=γ {P2}(G) . We show that γ(G)γ {P3}(G)γ t(G), where γ t(G) is the total domination number of G. For a nontrivial tree T, we show that γ {P3}(T)=γ t(T). We also define independent P 3-forming sets, give complexity results for the independent P 3-forming problem, and characterize the trees having an independent P 3-forming set.

Identiferoai:union.ndltd.org:ETSU/oai:dc.etsu.edu:etsu-works-15194
Date06 February 2003
CreatorsHaynes, Teresa W., Hedetniemi, Stephen T., Henning, Michael A., Slater, Peter J.
PublisherDigital Commons @ East Tennessee State University
Source SetsEast Tennessee State University
Detected LanguageEnglish
Typetext
SourceETSU Faculty Works

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