The Locating Chromatic Number of Pizza Graphs Containing a Single Path on the Outer Vertices
DOI:
https://doi.org/10.24252/msa.v13i2.60573Keywords:
locating chromatic number, Pizza graphs, single pathAbstract
In graph theory, the locating chromatic number refers to the minimum number of colours required to colour the vertices of a graph such that each vertex is uniquely identifiable by its own colour and the colours of its neighbouring vertices. This concept is associated with graph coloring, which entails assigning colors to a graph's vertices in such a way that no two adjacent vertices have the same color. It determines the minimum number of colours necessary to produce a proper vertex colouring. This research focuses on determining the locating chromatic number of Pizza graphs containing a single path on the outer vertices.
References
G. Chartrand, E. Salehi, and P. Zhang, “The partition dimension of a graph,” Aequationes Math., vol. 59, no. 1–2, pp. 45–54, 2000, doi: 10.1007/PL00000127.
V. Saenpholphat and P. Zhang, “Conditional resolvability in graphs: A survey,” Int. J. Math. Math. Sci., vol. 2004, no. 38, pp. 1997–2017, 2004, doi: 10.1155/S0161171204311403.
G. Chartrand, D. Erwin, M. A. Henning, P. J. Slater, and P. Zhang, “The locating-chromatic number of a graph,” Bull. Inst. Comb. it’s Appl., vol. 36, pp. 89–101, 2002.
A. Irawan, A. Asmiati, L. Zakaria, and K. Muludi, “The locating-chromatic number of origami graphs,” Algorithms, vol. 14, no. 6, pp. 1–15, 2021, doi: 10.3390/a14060167.
A. Irawan, Asmiati, S. Suharsono, and K. Muludi, “The locating-chromatic number of certain barbell origami graphs,” J. Phys. Conf. Ser., vol. 1751, no. 1, pp. 1–12, 2021, doi: 10.1088/1742-6596/1751/1/012017.
A. Irawan, Asmiati, L. Zakaria, K. Muludi, and U. Bernadhita, H, S, “Subdivision of Certain Barbell Operation of Origami Graphs has Locating-Chromatic Number Five,” vol. 21, no. 9, 2021.
A. Irawan, B. H. S. Utami, A. Nuryaman, and K. Muludi, “A Procedure for Determining The Locating Chromatic Number of An Origami Graphs,” IJCSNS Int. J. Comput. Sci. Netw. Secur., vol. 22, no. 9, pp. 2–5, 2022, [Online]. Available: https://doi.org/10.22937/IJCSNS.2022.22.9.5.
Asmiati, A. Irawan, A. Nuryaman, and K. Muludi, “The locating chromatic number for certain operation of origami graphs,” Math. Stat., vol. 11, no. 1, pp. 101–106, 2023, doi: 10.13189/ms.2023.110111.
W. D. A. Nur Hamzaha, Asmiatia, “Locating Chromatic Number for Corona Operation of Path Pn and Cycle Cm(m = 3,4),” Indones. J. Comb., vol. 8, no. 2, pp. 127–135, 2024, doi: 10.7546/nntdm.2019.25.2.190-198.
I. W. Sudarsana, F. Susanto, and S. Musdalifah, “The locating chromatic number for m-shadow of a connected graph,” Electron. J. Graph Theory Appl., vol. 10, no. 2, pp. 589–601, 2022, doi: 10.5614/ejgta.2022.10.2.18.
S. Nabila and A. N. M. Salman, “The rainbow connection number of origami graphs and pizza graphs,” Procedia Comput. Sci., vol. 74, no. December, pp. 162–167, 2015, doi: 10.1016/j.procs.2015.12.093.
N. M. Surbakti, D. Kartika, H. Nasution, and S. Dewi, “The Locating Chromatic Number for Pizza Graphs,” Sainmatika J. Ilm. Mat. dan Ilmu Pengetah. Alam, vol. 20, no. 2, pp. 126–131, 2023, doi: 10.31851/sainmatika.v20i2.13085.
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