Bilangan Dominasi Jarak-2 Graf Jahangir Jn,m

Article Sidebar

PDF
Published Jul 31, 2017

Main Article Content

Yayuk Wahyuni
Universitas Airlangga
M. Utomo Slamin Slamin

Abstract

Dalam graf  himpunan  dinamakan himpunan dominasi jarak-2 (distance-2 dominating set) jika setiap titik anggota  berada dalam jarak 2 dari paling sedikit satu titik dalam . Kardinalitas minimum diantara himpunan dominasi jarak-2 pada graf  dinamakan bilangan dominasi jarak–2 dari , dinotasikan dengan .  Penelitian ini bertujuan untuk menentukan bilangan dominasi jarak-2 dari graf Jahangir Jn,m, dengan menentukan suatu himpunan dominasi jarak-2 dan memperlihatkannya sebagai himpunan dominasi jarak-2 dengan kardinalitas minimum. Hasil penelitian ini menunjukkan bahwa untuk  berlaku  sedang untuk  yang lain bilangan dominasi jarak-2 Jn,m dapat dikelompokkan nilainnya dalam tiga kelompok bergantung pada nilai , semuanya berlaku untuk .

Article Details

How to Cite
WAHYUNI, Yayuk; UTOMO, M.; SLAMIN, Slamin. Bilangan Dominasi Jarak-2 Graf Jahangir Jn,m. Prosiding SI MaNIs (Seminar Nasional Integrasi Matematika dan Nilai-Nilai Islami), [S.l.], v. 1, n. 1, p. 606-610, july 2017. Available at: <http://conferences.uin-malang.ac.id/index.php/SIMANIS/article/view/411>. Date accessed: 01 apr. 2023.
ABNT APA BibTeX CBE EndNote - EndNote format (Macintosh & Windows) MLA ProCite - RIS format (Macintosh & Windows) RefWorks Reference Manager - RIS format (Windows only) Turabian
Issue
Vol 1 No 1 (2017): Prosiding SI MaNIs (Seminar Nasional Integrasi Matematika dan Nilai Islami )
Section
Mathematics
Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Copyright Notice

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

References

F. Tian and J.-M. Xu, "A note on distance domination numbers of graphs," Australas. J. Combin, vol. 43, pp. 181-190, 2009.
D. Meierling and L. Volkmann, "A lower bound for the distance k-domination number of trees," Results in Mathematics, vol. 47, pp. 335-339, 2005.
N. Sridharan, V. S. A. Subramanian and M. D. Elias, "Bounds on the distance two-domination number of a graph," Graphs and Combinatorics, vol. 18, pp. 667-675, 2002.
S. K. Vaidya and N. J. Kothari, "Distance k-domination of some path related graphs," International Journal of Mathematics and Soft Computing, vol. 4, pp. 1-5, 2014.
E. Prathibha, S. P. Missier and A. A. Kinsley, "Algorithms to Determine the Distance-t Dominating Sets of ES (n, k)," Procedia Computer Science, vol. 47, pp. 342-350, 2015.
T. W. Haynes, S. Hedetniemi and P. Slater, Fundamentals of domination in graphs, CRC Press, 1998.
G. Chartrand, "Dan Lesniak, L. 1996," Graph and Digraph.
D. A. Mojdeh and A. N. Ghameshlou, "Domination in Jahangir graph J2, m," Int. J. Contemp. Math. Sciences, vol. 2, pp. 1193-1199, 2007.
M. Ramachandran and N. Parvathi, "The Medium Domination Number of a Jahangir Graph J m, n," Indian Journal of Science and Technology, vol. 8, pp. 400-406, 2015.
R. Davila, C. Fast, M. Henning and F. Kenter, "Lower bounds on the distance domination number of a graph," arXiv preprint arXiv:1507.08745, 2015.