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Equivalence Domination in Graphs

For a graph G = (V, E), a subset S ⊆ V (G) is an equivalence dominating set if for every vertex v ∈ V (G) \ S, there exist two vertices u, w ∈ S such that the subgraph induced by {u, v, w} is a path. The equivalence domination number is the minimum cardinality of an equivalence dominating set of G, and the upper equivalence domination number is the maximum cardinality of a minimal equivalence dominating set of G. We explore relationships between total domination and equivalence domination. Then we determine the extremal graphs having large equivalence domination numbers.

Identiferoai:union.ndltd.org:ETSU/oai:dc.etsu.edu:etsu-works-15994
Date10 September 2013
CreatorsArumugam, S., Chellali, 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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