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Research Article

On the bounded partition dimension of some classes of convex polytopes

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Pages 2535-2548 | Received 01 Jul 2020, Published online: 01 Jul 2021

References

  • Amrullah, H., Assiyatun, E. T. Baskoro, S. Uttunggadewa, R. Simanjuntak, The Partition Dimension for a Subdivision of Homogeneous Caterpillars, AKCE International Journal of Graphs and Combinatorics, 10 3, 317-325, 2013.
  • L. M. Blumenthal, Theory and applications of distance geometry, Oxford University Press, 1953.
  • G. Chartrand, L. Eroh, M. A. Johnson, O. R. Oellermann, Resolvability in graphs and the metric dimension of a graph, Discrete Applied Mathematics, 105(1-3), 99-113, 2000. doi: 10.1016/S0166-218X(00)00198-0
  • G. Chartrand, E. Salehi, P. Zhang, The partition dimension of a graph, Aequationes Math., 59, 45–54, 2000. doi: 10.1007/PL00000127
  • V. Chvatal, Mastermind, Combinatorica, 3(3-4), 325-329, 1983. doi: 10.1007/BF02579188
  • F. Harary and R. A. Melter, On the metric dimension of a graph, Ars Combinatoria, 2, 191-195, 1976.
  • M. N. Husin, F. Asif, Z. Zahid, S. Zafar, On topological properties of some convex polytopes by using line operator on their subdivisions, Journal of Information and Optimization Sciences, 41(4)(2020), 891-903, DOI: 10.1080/02522667.2020.1744305.
  • M. Imran, S.A. Bokhary, A.Q. Baig, On families of convex polytopes with constant metric dimension, Computers and Mathematics with Applications, 60(9), 2629–2638, 2010. doi: 10.1016/j.camwa.2010.08.090
  • M. Imran, A.Q. Baig, A. Ahmad, Families of plane graphs with constant metric dimension, Utilitas Mathematics, 88, 43–57, 2012.
  • S. Khuller, B. Raghavachari, S. Rosenfeld, Landmarks in graphs, Discrete Applied Mathematics, 70(3) 217–229, 1996. doi: 10.1016/0166-218X(95)00106-2
  • P. Manuel, R. Bharati, I. Rajasingh, C. M. M, On minimum metric dimension of honeycomb networks, Journal of Discrete Algorithms, 6 (1), 20–27, 2008. doi: 10.1016/j.jda.2006.09.002
  • N. Mehreen, R. Farooq, S. Akhter, On partition dimension of fullerene graphs, AIMS Mathematics, 3(3), 343-352, 2018. doi: 10.3934/Math.2018.3.343
  • M.C. Monica, S. Santhakumar, Partition dimension of certain honeycomb derived networks, International Journal of Pure and Applied Mathematics 108(4), 809-818, 2016. doi: 10.12732/ijpam.v108i4.7
  • B. Rajan, A. William, I. Rajasingh, C. Grigorious, S. Stephen, On certain networks with partition dimension three, Proceedings of the International Conference on Mathematics in Engineering and Business Management 169-172, 2012.
  • J. A. Rodruez-Velàzquez, I. G. Yero and M. Lemanska, On the partition dimension of trees, Discrete Applied Mathematics, 166, 204-209, 2014. doi: 10.1016/j.dam.2013.09.026
  • J. A. Rodruez-Velàzquez, I. G. Yero and H. Fernau, On the partition dimension of unicyclic graphs, Bulletin mathématique de la Société des Sciences Mathématiques de Roumani, 57, 381-391, 2014.
  • P. J. Slater, Leaves of trees, Congress Numer, 14(1975), 549–559.

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