The product of the restrained domination numbers of a graph and its complement

Johannes H. Hattingh; Ernst J. Joubert

doi:10.1007/s10114-014-2492-1

The product of the restrained domination numbers of a graph and its complement

Johannes H. Hattingh, Ernst J. Joubert

Mathematics and Applied Mathematics

East Carolina University

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

Let G = (V,E) be a graph. A set S ⊆ V is a restrained dominating set if every vertex in V - S is adjacent to a vertex in S and to a vertex in V - S. The restrained domination number of G, denoted γ _r(G), is the smallest cardinality of a restrained dominating set of G. In this paper, we show that if G is a graph of order n ≥ 4, then γ_r(G)γ_r(Ḡ} ≤ 2n. We also characterize the graphs achieving the upper bound.

Original language	English
Pages (from-to)	445-452
Number of pages	8
Journal	Acta Mathematica Sinica, English Series
Volume	30
Issue number	3
DOIs	https://doi.org/10.1007/s10114-014-2492-1
Publication status	Published - Mar 2014

Keywords

Graph
Nordhaus-Gaddum
domination
restrained domination
upper bound

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1007/s10114-014-2492-1

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KW - Nordhaus-Gaddum

KW - domination

KW - restrained domination

KW - upper bound

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The product of the restrained domination numbers of a graph and its complement

Abstract

Keywords

ASJC Scopus subject areas

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