TY - JOUR

T1 - On classes of regular graphs with constant metric dimension

AU - Imran, Muhammad

AU - Bokhary, Syed Ahtsham ul Haq

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

Y1 - 2013/1

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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U2 - 10.1016/S0252-9602(12)60204-5

DO - 10.1016/S0252-9602(12)60204-5

M3 - Article

AN - SCOPUS:84871488725

SN - 0252-9602

VL - 33

SP - 187

EP - 206

JO - Acta Mathematica Scientia

JF - Acta Mathematica Scientia

IS - 1

ER -