Locating and paired-dominating sets in graphs

John McCoy; Michael A. Henning

doi:10.1016/j.dam.2009.06.019

Locating and paired-dominating sets in graphs

John McCoy, Michael A. Henning

University of KwaZulu-Natal

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

18 Citations (Scopus)

Abstract

In this paper, we continue the study of paired-domination in graphs introduced by Haynes and Slater [T.W. Haynes, P.J. Slater, Paired-domination in graphs, Networks 32 (1998), 199-206]. A paired-dominating set of a graph G with no isolated vertex is a dominating set S of vertices whose induced subgraph has a perfect matching. We consider paired-dominating sets which are also locating sets, that is distinct vertices of G are dominated by distinct subsets of the paired-dominating set. We consider three variations of sets which are paired-dominating and locating sets and investigate their properties.

Original language	English
Pages (from-to)	3268-3280
Number of pages	13
Journal	Discrete Applied Mathematics
Volume	157
Issue number	15
DOIs	https://doi.org/10.1016/j.dam.2009.06.019
Publication status	Published - 6 Aug 2009
Externally published	Yes

Keywords

Differentiating-paired-dominating set
Locating-paired-dominating set
Metric-locating-paired-dominating set

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1016/j.dam.2009.06.019

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AB - In this paper, we continue the study of paired-domination in graphs introduced by Haynes and Slater [T.W. Haynes, P.J. Slater, Paired-domination in graphs, Networks 32 (1998), 199-206]. A paired-dominating set of a graph G with no isolated vertex is a dominating set S of vertices whose induced subgraph has a perfect matching. We consider paired-dominating sets which are also locating sets, that is distinct vertices of G are dominated by distinct subsets of the paired-dominating set. We consider three variations of sets which are paired-dominating and locating sets and investigate their properties.

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KW - Locating-paired-dominating set

KW - Metric-locating-paired-dominating set

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ER -

Locating and paired-dominating sets in graphs

Abstract

Keywords

ASJC Scopus subject areas

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