Total domination in graphs with minimum degree three

Odile Favaron; Michael A. Henning; Christina M. Mynhart; Joël Puech

doi:10.1002/(SICI)1097-0118(200005)34:1<9::AID-JGT2>3.0.CO;2-O

Total domination in graphs with minimum degree three

Odile Favaron, Michael A. Henning, Christina M. Mynhart, Joël Puech

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

53 Citations (Scopus)

Abstract

A set S of vertices of a graph G is a total dominating set, if every vertex of V(G) is adjacent to some vertex in S. The total domination number of G, denoted by γt(G), is the minimum cardinality of a total dominating set of G. We prove that, if G is a graph of order n with minimum degree at least 3, then γt(G) ≤ 7n/13.

Original language	English
Pages (from-to)	9-19
Number of pages	11
Journal	Journal of Graph Theory
Volume	34
Issue number	1
DOIs	https://doi.org/10.1002/(SICI)1097-0118(200005)34:1<9::AID-JGT2>3.0.CO;2-O
Publication status	Published - May 2000
Externally published	Yes

Keywords

Bounds
Minimum degree three
Total domination number

ASJC Scopus subject areas

Geometry and Topology

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10.1002/(SICI)1097-0118(200005)34:1<9::AID-JGT2>3.0.CO;2-O

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AU - Henning, Michael A.

AU - Mynhart, Christina M.

AU - Puech, Joël

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Y1 - 2000/5

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AB - A set S of vertices of a graph G is a total dominating set, if every vertex of V(G) is adjacent to some vertex in S. The total domination number of G, denoted by γt(G), is the minimum cardinality of a total dominating set of G. We prove that, if G is a graph of order n with minimum degree at least 3, then γt(G) ≤ 7n/13.

KW - Bounds

KW - Minimum degree three

KW - Total domination number

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U2 - 10.1002/(SICI)1097-0118(200005)34:1<9::AID-JGT2>3.0.CO;2-O

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Total domination in graphs with minimum degree three

Abstract

Keywords

ASJC Scopus subject areas

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