22
Views
2
CrossRef citations to date
0
Altmetric
Research Article

On metric dimension of P(n, 2)ʘK1 graph

, , &

References

  • M. Bača, Labellings of two classes of convex polytopes, Utilitas Math. 34(1988); 24-31.
  • M. Bača, On magic labellings of convex polytopes, Annals Disc. Math. 51(1992); 13-16. DOI:10.1016/S0167-5060(08)70599-5
  • P. S. Buczkowski, G. Chartrand, C. Poisson, P. Zhang, On k-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.
  • M. A. Johnson, Structure-activity maps for visualizing the graph variables arising in drug design, J. Biopharm. Statist., 3(1993); 203-236. DOI:10.1080/10543409308835060
  • E. Jucovič, Convex polyhedra, Veda, Bratislava, 1981 (in Slovak).
  • S. Khuller, B. Raghavachari, A. Rosenfeld, Localization in graphs, Technical Report CS-TR-3326, University of Maryland at College Park, 1994.
  • S. Khuller, B. Raghavachari, A. Rosenfeld, Landmarks in graphs, Disc. Appl. Math:, 70(1996); 217-229. doi: 10.1016/0166-218X(95)00106-2
  • R. A. Melter, I. Tomescu, Metric bases in digital geometry, Computer Vision, Graphics, and Image Processing, 25(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.
  • P.J. Slater, Dominating and reference sets in graphs, J. Math. Phys. Sci., 22(1998); 445-455.
  • I. Tomescu, I. Javaid, On the metric dimension of the Jahangir graph, Bull. Math. Soc. Sci. Math. Roum., 50(98); 4(2007); 371-376
  • I. Tomescu, M. Imran, On metric and partition dimensions of some infinite regular graphs, Bull. Math. Soc. Sci. Math. Roum., 52(100); 4(2009); 461-472.
  • 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

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.