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 -