On classes of regular graphs with constant metric dimension

Muhammad Imran; Syed Ahtsham ul Haq Bokhary; Ali Ahmad; Andrea Semaničová-feňovčíková

doi:10.1016/S0252-9602(12)60204-5

On classes of regular graphs with constant metric dimension

Muhammad Imran
, Syed Ahtsham ul Haq Bokhary
, Ali Ahmad
, Andrea Semaničová-feňovčíková

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

46 Citations (Scopus)

Abstract

In this paper, we are dealing with the study of the metric dimension of some classes of regular graphs by considering a class of bridgeless cubic graphs called the flower snarks J_n, a class of cubic convex polytopes considering the open problem raised in [M. Imran et al., families of plane graphs with constant metric dimension, Utilitas Math., in press] and finally Harary graphs H_5,n by partially answering to an open problem proposed in [I. Javaid et al., Families of regular graphs with constant metric dimension, Utilitas Math., 2012, 88: 43-57]. We prove that these classes of regular graphs have constant metric dimension. It is natural to ask for the characterization of regular graphs with constant metric dimension.

Original language	English
Pages (from-to)	187-206
Number of pages	20
Journal	Acta Mathematica Scientia
Volume	33
Issue number	1
DOIs	https://doi.org/10.1016/S0252-9602(12)60204-5
Publication status	Published - Jan 2013
Externally published	Yes

Keywords

Basis
Convex polytope
Cubic graph
Flower snark
Metric dimension
Resolving set

ASJC Scopus subject areas

General Mathematics
General Physics and Astronomy

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10.1016/S0252-9602(12)60204-5

Cite this

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title = "On classes of regular graphs with constant metric dimension",

abstract = "In this paper, we are dealing with the study of the metric dimension of some classes of regular graphs by considering a class of bridgeless cubic graphs called the flower snarks Jn, a class of cubic convex polytopes considering the open problem raised in [M. Imran et al., families of plane graphs with constant metric dimension, Utilitas Math., in press] and finally Harary graphs H5,n by partially answering to an open problem proposed in [I. Javaid et al., Families of regular graphs with constant metric dimension, Utilitas Math., 2012, 88: 43-57]. We prove that these classes of regular graphs have constant metric dimension. It is natural to ask for the characterization of regular graphs with constant metric dimension.",

keywords = "Basis, Convex polytope, Cubic graph, Flower snark, Metric dimension, Resolving set",

author = "Muhammad Imran and Bokhary, \{Syed Ahtsham ul Haq\} and Ali Ahmad and Andrea Semani{\v c}ov{\'a}-fe{\v n}ov{\v c}{\'i}kov{\'a}",

note = "Funding Information: ∗Received September 5, 2011. This research is partially supported by National University of Sceinces and Technology (NUST), Islamabad, and grant of Higher Education Commission of Pakistan Ref. No: PM-IPFP/HRD/HEC/2011/3386 and support of Slovak VEGA Grant 1/0130/12. †Corresponding author: Muhammad IMRAN.",

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AU - Ahmad, Ali

AU - Semaničová-feňovčíková, Andrea

N1 - Funding Information: ∗Received September 5, 2011. This research is partially supported by National University of Sceinces and Technology (NUST), Islamabad, and grant of Higher Education Commission of Pakistan Ref. No: PM-IPFP/HRD/HEC/2011/3386 and support of Slovak VEGA Grant 1/0130/12. †Corresponding author: Muhammad IMRAN.

PY - 2013/1

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N2 - In this paper, we are dealing with the study of the metric dimension of some classes of regular graphs by considering a class of bridgeless cubic graphs called the flower snarks Jn, a class of cubic convex polytopes considering the open problem raised in [M. Imran et al., families of plane graphs with constant metric dimension, Utilitas Math., in press] and finally Harary graphs H5,n by partially answering to an open problem proposed in [I. Javaid et al., Families of regular graphs with constant metric dimension, Utilitas Math., 2012, 88: 43-57]. We prove that these classes of regular graphs have constant metric dimension. It is natural to ask for the characterization of regular graphs with constant metric dimension.

AB - In this paper, we are dealing with the study of the metric dimension of some classes of regular graphs by considering a class of bridgeless cubic graphs called the flower snarks Jn, a class of cubic convex polytopes considering the open problem raised in [M. Imran et al., families of plane graphs with constant metric dimension, Utilitas Math., in press] and finally Harary graphs H5,n by partially answering to an open problem proposed in [I. Javaid et al., Families of regular graphs with constant metric dimension, Utilitas Math., 2012, 88: 43-57]. We prove that these classes of regular graphs have constant metric dimension. It is natural to ask for the characterization of regular graphs with constant metric dimension.

KW - Basis

KW - Convex polytope

KW - Cubic graph

KW - Flower snark

KW - Metric dimension

KW - Resolving set

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On classes of regular graphs with constant metric dimension

Abstract

Keywords

ASJC Scopus subject areas

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