Pelabelan Koprima Pada Amalgamasi Graf Lengkap dan Graf Berlian

Hafif Komarullah, Slamin Slamin, Kristiana Wijaya

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.

Keywords


A coprime labeling; coprime number; amalgamation; complete and diamond graphs

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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 & 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, I Wui, “On the Amalgamation of Prime Graphs,” Bull. Malaysian Math. Soc, 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. Bača, and A. Semaničová-Feňovčíková, “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.




DOI: http://dx.doi.org/10.12962/limits.v21i1.13502

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Limits: Journal Mathematics and its Aplications by Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
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