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Graphs With Large Semipaired Domination Number

Let G be a graph with vertex set V and no isolated vertices. A subset S ⊆ V is a semipaired dominating set of G if every vertex in V \ S is adjacent to a vertex in S and S can be partitioned into two element subsets such that the vertices in each subset are at most distance two apart. The semipaired domination number γ pr2 (G) is the minimum cardinality of a semipaired dominating set of G. We show that if G is a connected graph G of order n ≥ 3, then γ pr2 (G) ≤ 32 n, and we characterize the extremal graphs achieving equality in the bound.

Identiferoai:union.ndltd.org:ETSU/oai:dc.etsu.edu:etsu-works-11321
Date01 January 2019
CreatorsHaynes, Teresa W., Henning, Michael A.
PublisherDigital Commons @ East Tennessee State University
Source SetsEast Tennessee State University
Detected LanguageEnglish
Typetext
SourceETSU Faculty Works

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