Total restrained domination in claw-free graphs with minimum degree at least two

Ernst J. Joubert

doi:10.1016/j.dam.2011.06.010

Total restrained domination in claw-free graphs with minimum degree at least two

Ernst J. Joubert

Mathematics and Applied Mathematics

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

5 Citations (Scopus)

Abstract

Let G=(V,E) be a graph. A set S⊆V is a total restrained dominating set if every vertex is adjacent to a vertex in S and every vertex in V-S is adjacent to a vertex in V-S. The total restrained domination number of G, denoted ^γtr(G), is the smallest cardinality of a total restrained dominating set of G. We will show that if G is claw-free, connected, has minimum degree at least two and G is not one of nine exceptional graphs, then ^γtr(G)≤4n/7.

Original language	English
Pages (from-to)	2078-2097
Number of pages	20
Journal	Discrete Applied Mathematics
Volume	159
Issue number	17
DOIs	https://doi.org/10.1016/j.dam.2011.06.010
Publication status	Published - 28 Oct 2011

Keywords

Claw-free
Domination
Total restrained domination

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1016/j.dam.2011.06.010

Cite this

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abstract = "Let G=(V,E) be a graph. A set S⊆V is a total restrained dominating set if every vertex is adjacent to a vertex in S and every vertex in V-S is adjacent to a vertex in V-S. The total restrained domination number of G, denoted γtr(G), is the smallest cardinality of a total restrained dominating set of G. We will show that if G is claw-free, connected, has minimum degree at least two and G is not one of nine exceptional graphs, then γtr(G)≤4n/7.",

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AB - Let G=(V,E) be a graph. A set S⊆V is a total restrained dominating set if every vertex is adjacent to a vertex in S and every vertex in V-S is adjacent to a vertex in V-S. The total restrained domination number of G, denoted γtr(G), is the smallest cardinality of a total restrained dominating set of G. We will show that if G is claw-free, connected, has minimum degree at least two and G is not one of nine exceptional graphs, then γtr(G)≤4n/7.

KW - Claw-free

KW - Domination

KW - Total restrained domination

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ER -

Total restrained domination in claw-free graphs with minimum degree at least two

Abstract

Keywords

ASJC Scopus subject areas

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