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Journal of Discrete Mathematical Sciences and Cryptography Volume 24, 2021 - Issue 2: Applied Mathematics, Mathematical Chemistry, Computations and Graph Theory
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Research Article

Fault-tolerant metric dimension of P(n, 2)ʘK1 graph

Zubair Ahmad1 Department of Mathematics, The University of Lahore, Pakpattan Campus, PakistanCorrespondence[email protected]
,
Maqbool Ahmad Chaudhary2 Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan E-mail: [email protected]
,
Abdul Qudair Baig3 Department of Mathematics and Statistics, Institute of Southern Punjab, Multan, Pakistan E-mail: [email protected]
&
Manzoor Ahmad Zahid4 Department of Mathematics, COMSATS Institute of Information Technology, Sahiwal Campus, Pakistan E-mail: [email protected]
Pages 647-656 | Published online: 08 Apr 2021

References

  • Z. Ahmad, M. Ahmad Ch., A. Q. Baig, M. A. Zahid, On MetricDimension of P(n, 2)ʘK1 Graph, submitted to Journal of Discrete Mathematical Sciences and Cryptography.
  • P. S. Buczkowski, G. Chartrand, C. Poisson, P. Zhang, Onk-dimensional graphs and their bases, Periodica Math. Hung., 46(1), (2003), 9-15. DOI:10.1023/A:1025745406160
  • J. Caceres, C. Hernando, M. Mora, I. M. Pelayo, M. L. Puertas, C. Seara, D.R. Wood, On the metric dimension of some families of graphs, Electronic Notes in Disc. Math., 22(2005), 129-133. DOI:10.1016/j.endm.2005.06.023
  • J. Caceres, C. Hernando, M. Mora, I. M. Pelayo, M. L. Puertas, C. Seara, D.R. Wood, On the metric dimension of Cartesian product of graphs, SIAM J. Disc. Math., 2(21), (2007), 423-441. DOI:10.1137/050641867
  • G. Chartrand, P. Zhang, The theory and applications of resolvability in graphs, Congress. Numer., 160(2003), 47-68.
  • G. Chartrand, L. Eroh, M. A. Johnson, O. R. Oellermann, Resolvability in graphs and metric dimension of a graph, Disc. Appl. Math., 105(2000), 99-113. https://core.ac.uk/download/pdf/82498269.pdf doi: 10.1016/S0166-218X(00)00198-0
  • M. R. Garey, D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman, New York, 1979.
  • F. Harary, R. A. Melter, On the metric dimension of a graph, Ars Combin., 2(1976), 191-195.
  • M. Imran, A.Q. Baig, A. Ahmad, Families of plane graphs with constant metric dimension, Utilitas Math., 88(2012), 43-57.
  • M. Imran, A.Q. Baig, M. K. Shafiq, I. Tomescu, On metric dimension of generalized Petersen graphs P(n, 3), to appear in Ars Combin.
  • I. Javaid, M. T. Rahim, K. Ali, Families of regular graphs with constant metric dimension, Utilitas Math., 75(2008), 21-33.
  • R. A. Melter, I. Tomescu, Metric bases in digital geometry, Computer Vision, Graphics, and Image Processing, 25(1), (1984), 113-121. DOI:10.1016/0734-189X(84)90051-3
  • E. Mphako-Banda, Some polynomials of flower graphs, International Math. Forum, 2(51)(2007), 2511-2518. doi: 10.12988/imf.2007.07221
  • O.R. Oellermann, J. Peters-Fransen, Metric dimension of Cartesian products of graphs, Utilitas Math., 69(2006), 33-41.
  • P. J. Slater, Leaves of trees, Congress. Numer., 14(1975), 549-559.
  • I. Tomescu, I. Javaid, On the metric dimension of the Jahangir graph, Bull. Math.Soc. Sci. Math. Roum., 50(98), (2007), 371-376. https://arxiv.org/pdf/1905.03975.pdf
  • L. Yan, Y. Li, X. Zhang, M. Saqlain, S. Zafar, M.R. Farahani. 3-total edge product cordial labeling of some new classes of graphs. Journal of Information & Optimization Sciences, 39(3), 2018, 705–724. DOI:10.1080/02522667.2017.1417727
  • I. Rosyida, E. Ningrum, Mulyono, D. Indriati. On Total Vertex and Edge Irregularity Strengths. Journal of Discrete Mathematical Sciences and Cryptography. 23(6), 2020, 1335–1358. DOI:10.1080/09720529.2020.1820704
  • I. Rosyida, Mulyono, D. Indriati. On Total Vertex Irregularity Strengths of Uniform Cactus Chains. Journal of Discrete Mathematical Sciences and Cryptography. 23(6), 2020, 1369–1380. DOI:10.1080/09720529.2020.1830562
  • M.A. Mohammed, A.J. Munshid, H.M.A. Siddiqui, M.R. Farahani. Computing the metric and partition dimension of tessellation of plane by boron nanosheets. Eurasian Chem. Commun. 2(2020) 1064-1071. DOI:10.22034/ECC.2020.251927.1083

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