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Subdivision of Certain Barbell Operation of Origami Graphs has Locating-Chromatic Number Five

  • Irawan, Agus (Information System, STMIK Pringsewu) ;
  • Asmiati, Asmiati (Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Lampung) ;
  • Zakaria, La (Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Lampung) ;
  • Muludi, Kurnia (Computer Sciences, Faculty of Mathematics and Natural Sciences, University of Lampung) ;
  • Utami, Bernadhita Herindri Samodra (Information System, STMIK Pringsewu)
  • Received : 2021.09.05
  • Accepted : 2021.09.20
  • Published : 2021.09.30

Abstract

The locating-chromatic number denote by 𝛘𝐿(G), is the smallest t such that G has a locating t-coloring. In this research, we determined locating-chromatic number for subdivision of certain barbell operation of origami graphs.

Keywords

Acknowledgement

This work was partially supported by a research grant from DRPM Dikti 2021.

References

  1. G. Chartrand, P. Zhang, E. Salehi, On the partition dimension of a graph, Congressus Numerantium, vol.130, pp.157-168, 1998.
  2. V. Saenpholphat and P. Zhang, Conditional resolvability: a survey, International Journal of Mathematics and Mathematical Sciences, vol.38, pp.1997-2017, 2004. https://doi.org/10.1155/S0161171204311403
  3. G. Chartrand and P. Zhang, The theory and applications of resolvability in graphs. A survey,Congr.Numer.160, pp.47-68, 2003.
  4. M. Johnson, Conditional resolvability: a survey, Structure-activity maps for visualizing the graph variables arising in drug design, Journal of Biopharmaceutical Statistics, vol.3, no.2, pp.203-236, 1993. https://doi.org/10.1080/10543409308835060
  5. G. Chartrand, D. Erwin, M. A, Henning, P. J. Slater, P. Zhang, The locating-chromatic number of a graphs, Bulletin of the Institute of Combinatorics and its Applications, vol. 36, pp.89-101, 2002.
  6. G. Chartrand, D. Erwin, M. A, Henning,P. J. Slater, P. Zhang, Graf of order n with locating-chromatic number n - 1, Discrate Mathematics, vol.269, no.1-3, pp.65 - 79, 2003 https://doi.org/10.1016/S0012-365X(02)00829-4
  7. E. T. Baskoro and Asmiati, Characterizing all trees with locating-chromatic number 3, Electronic Journal of Graph Theory and Applications (EJGTA), vol.1, no.2, pp.109-117, 2013. https://doi.org/10.5614/ejgta.2013.1.2.4
  8. A. Behtoei, M. Anbarloei, The locating chromatic number of the join of graphs, Bulletin of the Iranian Mathematical Society, vol.40, no.6, pp.1491-1504, 2014.
  9. I. A. Purwasih, E. T. Baskoro, H. Assiyatun, D. Suprijanto, The bounds on the locating-chromatic number for a subdivision of a graph on one edge, Procedia Computer Science, vol.74, pp.84 - 88, 2015. https://doi.org/10.1016/j.procs.2015.12.080
  10. D. Welyyanti , E. T. Baskoro, R. Simanjuntak, S. Uttunggadewa, On locating-chromatic number for graphs with dominant vertices, Procedia Computer Science, vol.74, pp.89-92, 2015. https://doi.org/10.1016/j.procs.2015.12.081
  11. Asmiati, On the locating-chromatic numbers of nonhomogeneous caterpillars and firecrackers graphs, Far East Journal of Mathematical Sciences (FJMS), vol.100, no.8, pp.1305-1316, 2016. https://doi.org/10.17654/MS100081305
  12. Asmiati, I. K. G. Yana, and L. Yulianti, On The Locating Chromatic Number of Certain Barbell Graphs, International Journal of Mathematics and Mathematical Sciences, pp.1-5, 2018.
  13. A. Irawan, Asmiati, S. Suharsono, K. Muludi, The locating-chromatic number for certain operation of generalized petersen graphs sP(4,2), Journal of Physics: Conference Series, 1338, pp.1-6, 2019.
  14. A. Irawan, Asmiati, S. Suharsono, K. Muludi, L. Zakaria, Certain operation of generalized petersen graphs having locating-chromatic number five, Advances and Applications in Discrete Mathematics, vol.24, no.2, pp.83-97, 2020. https://doi.org/10.17654/dm024020083
  15. A. Irawan, Asmiati, L. Zakaria, K. Muludi, The locating-chromatic number of origami graphs, Algorithms, vol.14, no.167, pp.1-15, 2021.
  16. A. Irawan, Asmiati, S. Suharsono, K. Muludi, The Locating-Chromatic Number of Certain Barbell Origami Graphs, Journal of Physics: Conference Series, 1750, pp.1-13, 2021.
  17. Asmiati, E. T. Baskoro, Characterizing all graphs containing cycles with locating-chromatic number 3, AIP Conference Proceedings, 1450, pp.351-357, 2012.
  18. S. Nabila, A. N. M.Salman, The Rainbow Conection Number of Origami Graphs and Pizza Graphs, Procedia Computer Science, 74, pp.162-167, 2015. https://doi.org/10.1016/j.procs.2015.12.093