Pelabelan Koprima Pada Amalgamasi Graf Lengkap dan Graf Berlian

Authors

  • Hafif Komarullah Program Studi Sistem Informasi, Universitas Jember
  • Slamin Program Studi Sistem Informasi, Universitas Jember
  • Kristiana Wijaya Program Studi Sistem Informasi, Universitas Jember

Keywords:

A coprime labeling, minimum coprime number

Abstract

Pelabelan koprima pada graf berorder n adalah pemberian label berbeda pada setiap titik di graf sedemikian sehingga setiap dua titik yang bertetangga mempunyai label yang relatif prima. Sebuah graf disebut graf prima jika label yang digunakan adalah n bilangan bulat positif pertama. Permasalahan pada pelabelan koprima adalah mendapatkan nilai terkecil dari kemungkinan label terbesar yang digunakan sehingga sehingga memenuhi aturan pelabelan koprima, yang dinamakan bilangan koprima. Pada paper ini dibahas bilangan koprima dari graf hasil amalgamasi titik pada graf lengkap. Selanjutnya dicari bilangan koprima dari graf berlian dan graf hasil amalgamasi titik graf berlian.

References

D. M. Burton, Elementary Number Theory, 5th ed. New York: McGraw-Hill, 2002.

A. H. Berliner, J. Hook, A. Mbirika, N. Dean, A. Marr, and C. D. Mcbee, Coprime and Prime Labelings of Graphs, Journal of Integer Sequences, vol. 19, 2016. Online. Available: https://cs.uwaterloo.ca/journals/JIS/VOL19/Mbirika/mbi3.pdf

S. Ashokkumar and S. Maragathavalli, Prime Labelling of Some Special Graphs, IOSR Journal of Mathematics, vol. 11, no. 1, pp. 1–5, 2015, doi: 10.9790/5728-11110105. Online. Available: https://iosrjournals.org/iosr-jm/papers/Vol11-issue1/Version-1/A011110105.pdf

D. M. T. B. Dissanayake, R. A. S. T. Abeysekara, K. D. E. Dhananjaya, A. A. I. Perera, and P. G. R. S. Ranasinghe, Prime Labeling of Complete Tripartite Graphs of the Form K(1,m,n), vol. 130, pp. 53092–53094, 2019. Online. Available: https://www.researchgate.net/publication/333357422_Prime_labeling_of_complete_tripartite_graphs_of_the_form_K_1mn

N. Dean, Proof of the prime ladder conjecture, Integers, vol. 17, p. A40, 2017. Online. Available: http://math.colgate.edu/~integers/r40/r40.pdf

N. Ramya, K. Rangarajan, and R. Sattanathan, On Prime Labeling of Some Classes of Graphs, International Journal of Computer Applications, vol. 44, no. 4, pp. 975–8887, 2012. Online. Available: https://research.ijcaonline.org/volume44/number4/pxc3878320.pdf

S. Meena and K. Vaithilingam, Prime Labeling of Friendship Graphs, International Journal of Engineering Research and Technology (IJERT), vol. 1, 2012. Online. Available: https://www.ijert.org/research/prime-labeling-of-friendship-graphs-IJERTV1IS10257.pdf

S. K. Vaidya and U. M. Prajapati, Some New Results on Prime Graphs, Open Journal of Discrete Mathematics, vol. 02, no. 03, pp. 99–104, 2012, doi: 10.4236/ojdm.2012.23019. Online. Available: https://www.scirp.org/pdf/OJDM20120300007_69764759.pdf

J. Asplund and N. B. Fox, Minimum Coprime Labelings for Operations on Graphs, Jul. 2017. Online. Available: http://arxiv.org/abs/1707.04471

J. Asplund and N. Bradley Fox, Minimum Coprime Labelings of Generalized Petersen and Prism Graphs, Journal of Integer Sequences, vol. 24, no. 3, pp. 1–21, 2019. Online. Available: https://cs.uwaterloo.ca/journals/JIS/VOL24/Fox/fox11.pdf

C. Lee, Minimum Coprime Graph Labelings, Journal of Integer Sequences, vol. 23, no. 11, pp. 1–15, 2020. Online. Available: https://cs.uwaterloo.ca/journals/JIS/VOL23/Lee/lee7.pdf

J. Y. S. M. Lee and I. Wui, On the Amalgamation of Prime Graphs, Bulletin of the Malaysian Mathematical Society, vol. 11, pp. 59–67, 1988.

H. Komarullah, Slamin, and K. Wijaya, A Minimum Coprime Number for Amalgamation of Wheel, in Advances in Computer Science Research, volume 96, Proceedings of the International Conference on Mathematics, Geometry, Statistics, and Computation, 2022, pp. 53–57. https://doi.org/10.2991/acsr.k.220202.012

J. A. Gallian, A Dynamic Survey of Graph Labeling, The Electronic Journal of Combinatorics, p. 6, 2017. Online. Available: https://www.combinatorics.org/files/Surveys/ds6/ds6v20-2017.pdf

N. Hinding, D. Firmayasari, H. Basir, M. Baca, and A. Semanicova-Fenovcikova, On Irregularity Strength of Diamond Network, AKCE International Journal of Graphs and Combinatorics, vol. 15, no. 3, pp. 291–297, Dec. 2018. https://doi.org/10.1016/j.akcej.2017.10.003

Sukirman, Teori Bilangan, 1st ed. Tanggerang Selatan: Universitas Terbuka, 2016.

Downloads

Published

2024-03-15

How to Cite

Hafif Komarullah, Slamin, & Kristiana Wijaya. (2024). Pelabelan Koprima Pada Amalgamasi Graf Lengkap dan Graf Berlian. Limits: Journal of Mathematics and Its Applications, 21(1), 1–12. Retrieved from https://journal.its.ac.id/index.php/limits/article/view/5691