R-Sets and Metric Dimension of Necklace Graphs

Ioan Tomescu; Muhammad Imran

doi:10.12785/AMIS/010109

R-Sets and Metric Dimension of Necklace Graphs

Ioan Tomescu
, Muhammad Imran

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

1 Citation (Scopus)

Abstract

The R-set relative to a pair of distinct vertices of a connected graph G is the set of vertices whose distances to these vertices are distinct. In this paper R-sets are used to show that metric dimension dim(Ne_n) = 3 when n is odd and 2 otherwise, where Ne_n is the necklace graph of order 2n + 2. It is also shown that the exchange property of the bases in a vector space does not hold for minimal resolving sets of Nen if n is even.

Original language	English
Pages (from-to)	63-67
Number of pages	5
Journal	Applied Mathematics and Information Sciences
Volume	9
Issue number	1
DOIs	https://doi.org/10.12785/AMIS/010109
Publication status	Published - Jan 2015
Externally published	Yes

Keywords

Metric dimension
R-set
diameter
exchange property
necklace graph

ASJC Scopus subject areas

Analysis
Numerical Analysis
Computer Science Applications
Computational Theory and Mathematics
Applied Mathematics

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10.12785/AMIS/010109

Cite this

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AB - The R-set relative to a pair of distinct vertices of a connected graph G is the set of vertices whose distances to these vertices are distinct. In this paper R-sets are used to show that metric dimension dim(Nen) = 3 when n is odd and 2 otherwise, where Nen is the necklace graph of order 2n + 2. It is also shown that the exchange property of the bases in a vector space does not hold for minimal resolving sets of Nen if n is even.

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KW - R-set

KW - diameter

KW - exchange property

KW - necklace graph

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R-Sets and Metric Dimension of Necklace Graphs

Abstract

Keywords

ASJC Scopus subject areas

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