DETERMINATION OF THE RESTRAINED DOMINATION NUMBER ON VERTEX AMALGAMATION AND EDGE AMALGAMATION OF THE PATH GRAPH WITH THE SAME ORDER

  • Landerius Maro Program Studi Matematika,Fakultas Matematika dan Ilmu Pengetahuan Alam, Universitas Tribuana Kalabahi
  • Amelia Sanga Program Studi Matematika,Fakultas Matematika dan Ilmu Pengetahuan Alam, Universitas Tribuana Kalabahi
  • Mia E Tuaty Program Studi Matematika,Fakultas Matematika dan Ilmu Pengetahuan Alam, Universitas Tribuana Kalabahi
Keywords: Restrained Dominating Number, Vertex Amalgamation, Edges Amalgamation, Path Graph

Abstract

Graph theory is a mathematics section that studies discrete objects. One of the concepts studied in graph theory is the restrained dominating set which aims to find the restrained dominating number. This research was conducted by examining the graph operation result of the vertex and edges amalgamation of the path graph in the same order. The method used in this research is the deductive method by using existing theorems to produce new theorems that will be proven deductively true. This research aimed to determine the restrained dominating number in vertex and edges amalgamation of the path graph in the same order. The results obtained from this study are in the form of the theorem about the restrained dominating number of vertex and edges amalgamation of the path graph in the same order, namely: for , , and for , .

Downloads

Download data is not yet available.

References

R. Munir, Matematika Diskrit, Ketiga [Discrete Mathematics, Third]. Bandung: Informatika Bandung, 2012.

R. Adawiyah, “Penentuan Bilangan Dominasi Sisi Pada Graf Hasil Operasi Produk Tensor,” ["Determining the Domination of the Edge Number in the Graph of the Operating Result of the Tensor Product,"] Progr. Magister, Jur. Mat. Fak. Mat. dan Ilmu Pengetah. Alam, Inst. Teknol. Sepuluh Nop. Surabaya, 2016.

L. Maro, “Himpunan Dominasi Terkendali pada Korona Graf Lintasan dengan Graf Lintasan, Graf Siklus dengan Graf Siklus, dan Graf Lengkap dengan Graf Lengkap,” ["Restrained dominating set in Coronary of Path Graph with Path Graph, Cycle Graph with Cycle Graph, and Complete Graph with Complete Graph,"] Progr. Stud. Magister Mat. Fak. Mat. dan Ilmu Pengetah. Alam, Sekol. Pascasarjana, Univ. Hasanuddin Makassar, 2017.

G. S. Domke, J. H. Hattingh, S. T. Hedetniemi, R. C. Laskar, and L. R. Markus, “Restrained domination in graphs,” Discrete Math., vol. 203, pp. 61–69, 1999, [Online]. Available: www.elsevier.com/locate/disc.

H. D. Saputro, “Dominating Set pada Hasil Operasi Graf Khusus dan Aplikasinya,” ["Dominating Sets on the Results of Special Graph Operations and Their Applications,"] Jur. Mat. Fak. Mat. dan Ilmu Pengetah. Alam, Univ. Jember, 2015.

E. L. Enriquez, “Secure Restrained Domination in the Join and Corona of Graphs,” 2016. [Online]. Available: http://www.ripublication.com/gjpam.htm.

R. C. Alota and E. L. Enriquez, “On Disjoint Restrained Domination in Graphs 1,” 2016. [Online]. Available: http://www.ripublication.com/gjpam.htm.

D. K. Thakkar and & D. D. Pandya, “CRITICAL GRAPHS IN RESTRAINED DOMINATION.”

J. H. Hattingh and E. J. Joubert, “Restrained domination in claw-free graphs with minimum degree at least two,” Graphs Comb., vol. 25, no. 5, pp. 693–706, Feb. 2010, doi: 10.1007/s00373-010-0883-3.

J. H. Hattingh and E. J. Joubert, “Restrained domination in cubic graphs,” J. Comb. Optim., vol. 22, no. 2, pp. 166–179, Aug. 2011, doi: 10.1007/s10878-009-9281-2.

V. R. Kulli, “Inverse and Disjoint Restrained Domination in Graphs,” 2016. [Online]. Available: www.researchmathsci.org.

X. Chen, Vy. Jiaiig, D. Xiec, and Y. Wang, “Total restrained domination in unicyclic graphs,” Ars Comb., vol. 148, pp. 149–165, Jan. 2020.

S. R. Canoy, “Restrained domination in graphs under some binary operations,” Appl. Math. Sci., vol. 8, no. 121–124, pp. 6025–6031, 2014, doi: 10.12988/ams.2014.48597.

R. Ardiyansah and Darmaji, “Bilangan Kromatik Graf Hasil Amalgamasi Dua Buah Graf,” J. Sains dan Seni POMITS, vol. 02, no. 01, pp. 1–5, 2013.

R. Diestel, Graph Theory, Electronic. New York: Springer - Verlag Heidelberg, 2005.

J. H. Hattingh et al., “RESTRAINED DOMINATION IN UNICYCLIC GRAPHS,” 2009.

Published
2022-06-01
How to Cite
[1]
L. Maro, A. Sanga, and M. Tuaty, “DETERMINATION OF THE RESTRAINED DOMINATION NUMBER ON VERTEX AMALGAMATION AND EDGE AMALGAMATION OF THE PATH GRAPH WITH THE SAME ORDER”, BAREKENG: J. Math. & App., vol. 16, no. 2, pp. 421-426, Jun. 2022.