Upper bounds on the paired-domination number

Xue gang Chen; Wai Chee Shiu; Wai Hong Chan

doi:10.1016/j.aml.2007.10.029

Upper bounds on the paired-domination number

Xue gang Chen^*
, Wai Chee Shiu
, Wai Hong Chan

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

11 Citations (Scopus)

Abstract

A set S of vertices in a graph G is a paired-dominating set of G if every vertex of G is adjacent to some vertex in S and the subgraph induced by S contains a perfect matching. The minimum cardinality of a paired-dominating set of G is the paired-domination number of G, denoted by γ_{p r} (G). In this work, we present several upper bounds on the paired-domination number in terms of the maximum degree, minimum degree, girth and order.

Original language	English
Pages (from-to)	1194-1198
Number of pages	5
Journal	Applied Mathematics Letters
Volume	21
Issue number	11
DOIs	https://doi.org/10.1016/j.aml.2007.10.029
Publication status	Published - Nov 2008

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Girth
Maximum degree
Minimum degree
Paired-domination number

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10.1016/j.aml.2007.10.029

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title = "Upper bounds on the paired-domination number",

abstract = "A set S of vertices in a graph G is a paired-dominating set of G if every vertex of G is adjacent to some vertex in S and the subgraph induced by S contains a perfect matching. The minimum cardinality of a paired-dominating set of G is the paired-domination number of G, denoted by γp r (G). In this work, we present several upper bounds on the paired-domination number in terms of the maximum degree, minimum degree, girth and order.",

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author = "Chen, \{Xue gang\} and Shiu, \{Wai Chee\} and Chan, \{Wai Hong\}",

note = "Funding Information: This work was partially supported by the CERG Research Grant Council of Hong Kong and the Faculty Research Grant of Hong Kong Baptist University. It was supported by a Doctoral Research Grant of North China Electric Power University (200722026).",

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AU - Shiu, Wai Chee

AU - Chan, Wai Hong

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N2 - A set S of vertices in a graph G is a paired-dominating set of G if every vertex of G is adjacent to some vertex in S and the subgraph induced by S contains a perfect matching. The minimum cardinality of a paired-dominating set of G is the paired-domination number of G, denoted by γp r (G). In this work, we present several upper bounds on the paired-domination number in terms of the maximum degree, minimum degree, girth and order.

AB - A set S of vertices in a graph G is a paired-dominating set of G if every vertex of G is adjacent to some vertex in S and the subgraph induced by S contains a perfect matching. The minimum cardinality of a paired-dominating set of G is the paired-domination number of G, denoted by γp r (G). In this work, we present several upper bounds on the paired-domination number in terms of the maximum degree, minimum degree, girth and order.

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KW - Minimum degree

KW - Paired-domination number

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DO - 10.1016/j.aml.2007.10.029

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JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

IS - 11

ER -

Upper bounds on the paired-domination number

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