Bilangan Dominasi-Lokasi pada Graf Hasil Kali Operasi Comb Graf Lintasan dan Graf Siklus

  • Aswan Anggun Pribadi Institut Teknologi Sumatera
  • Muhammad Dhani Program Studi Matematika, Jurusan Sains, Institut Teknologi Sumatera
  • Anastasia Lia Dwi Prestanti Program Studi Matematika, Jurusan Sains, Institut Teknologi Sumatera

Abstract

Dominating set of graph G is subset D⊆V(G) which for every vertex v∈V(G)\D those vertices has neighbour in D. If for every pairs of vertice x and y their neighbour set different than we called D locating-dominating set. As for the minimum cardinality of possible dominating set of G is called the locating-dominating number of G. We determine the value of the locating-dominating number for comb product path (Pn) and cycle (Cn) graph.

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References

[1] P. J. Slater, “Domination and location in acyclic graphs,” Networks, vol. 17, no. 1, pp. 55–64, 1987, doi: https://doi.org/10.1002/net.3230170105.
[2] P. J. Slater, “Dominating and Reference Sets in a Graph,” Journal of Mathematical and Physical Sciences, vol. 22, no. 4, 1988, pp. 445-455.
[3] M. Henning and O. Oellermann, “Metric-Locating-Dominating Sets in Graphs.,” Ars Comb., vol. 73, Jan. 2004.
[4] S. J. Seo and P. J. Slater, “Open neighborhood locating-dominating sets,” Australasian Journal of Combinatorics, vol. 46, pp. 109–119, Jan. 2010.
[5] M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-completeness. Freeman, 1979. [Online]. Available: https://books.google.co.id/books?id=fjxGAQAAIAAJ
[6] J. Cáceres, M. C. Hernando, M. Mora, I. Pelayo, and M. Puertas, “Locating-dominating codes: Bounds and extremal cardinalities,” Appl Math Comput, vol. 220, pp. 38–45, Jan. 2013.
[7] M. del Carmen Hernando Martín, M. M. Giné, and I. M. P. Melero, “Locating domination in graphs and their complements,” 2013
[8] A. Pribadi and S. Saputro, “On locating-dominating number of comb product graphs,” Indonesian Journal of Combinatorics, vol. 4, p. 27, Jan. 2020, doi: 10.19184/ijc.2020.4.1.4.
Published
2023-01-28
How to Cite
PRIBADI, Aswan Anggun; DHANI, Muhammad; PRESTANTI, Anastasia Lia Dwi. Bilangan Dominasi-Lokasi pada Graf Hasil Kali Operasi Comb Graf Lintasan dan Graf Siklus. Indonesian Journal of Applied Mathematics, [S.l.], v. 2, n. 2, p. 74-76, jan. 2023. ISSN 2774-2016. Available at: <https://journal.itera.ac.id/index.php/indojam/article/view/1039>. Date accessed: 18 may 2024. doi: https://doi.org/10.35472/indojam.v2i2.1039.