Authors:
T.W. Haynes, M.A. Henning
Title:
Graphs with large semipared domination number
Source:
Discussiones Mathematicae Graph Theory
Received 07.08.2017, Revised 24.03.2018, Accepted 03.04.2018, doi: 10.7151/dmgt.2143

Abstract:
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 \setminus 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 \semiP(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 \semiP(G) \le \frac{2}{3}n, and we characterize the extremal graphs achieving equality in the bound.
Keywords:
paired-domination, semipaired domination

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