Pelabelan Total Tak Reguler Sisi pada Graf Direction, Graf Direction Right, dan Graf Heart

  • Juli Setiawati Universitas Sulawesi Barat
  • Meryta Febrilian Fatimah Universitas Sulawesi Barat
  • Darma Ekawati Universitas Sulawesi Barat
DOI: https://doi.org/10.30605/proximal.v6i2.2559
Keywords: kekuatan total tak reguler sisi, pelabelan total tak reguler sisi, graf direction, graf direction right, graf heart

Abstract

Pelabelan graf adalah suatu fungsi yang memasangkan elemen-elemen graf ke suatu bilangan bulat positif. Graf dapat dituliskan dengan G = (V(G), E(G)) dimana V(G) merupakan himpunan titik tak kosong dan E(G) merupakan himpunan sisi. Suatu pemetaan  f : V(G)  E(G) {1,2,3,…….k} untuk suatu bilangan bulat k, disebut pelabelan k total tak reguler sisi jika untuk setiap dua sisi e1 = u1v1 dan e2 = u2v2  yang berbeda, memiliki bobot sisi yang berbeda, yakni wtf (e1) = wtf (e2). Nilai k terkecil pada pelabelan k total tak reguler sisi disebut sebagai kekuatan total tak reguler sisi pada graf G dan disimbolkan dengan tes(G). Tujuan penelitian ini adalah untuk menentukan nilai kekuatan total tak reguler sisi pada graf direction, graf direction right, dan graf heart serta melabeli graf tersebut menggunakan pelabelan total tak reguler sisi. Metode yang digunakan dalam penulisan tugas akhir ini adalah studi literatur. Berdasarkan hasil penelitian, diperoleh pola pelabelan dan nilai kekuatan total tak reguler sisi dari ketiga graf tersebut, yang berturut-turut mempunyai nilai tes(Dn)= 6n + 1, tes(Drn)= 3n + 1, dan tes(Hn)= 4n + 1, untuk n 1.

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References

Bača, M., Jendrol', S., dkk. (2007). On Irregular Total Labellings. Journal of Discrete Mathematics, Vol. 307, hal. 1378–1388.

Bondy, J. A., & Murty, U. S. R. (1976). Graph Theory with Applications. New York: Elsevier Science Publishing.

Gallian, J. A. (2017). A Dynamic Survey of Graph Labeling. The Electronic Journal of Combinatorics, Vol. 18, #DS6.

J., & Jendrol', S. (2006). Total Edge Irregularity Strength of Trees. Journal of Discussiones Mathematicae, Vol. 26, hal. 449–456.

Khotimah, H., dkk. (2019). Kekuatan Total Tak Reguler Sisi Graf Double Fan dan Graf-Graf Terkait Graf Double Fan. Jurnal Matematika Thales (JMT), Vol. 01-01.

Marsudi. (2016). Teori Graf, Ed. 1. Malang: Universitas Brawijaya Press.

Munir, R. (2010). Matematika Diskrit, Ed. 3. Bandung: Informatika Bandung.

Sancoko, S. D., dkk. (2017). Kekuatan Tak Reguler Sisi Total Pada Graf Umbrella Dan Graf Fraktal, hal 37–42.

Wallis, W. D. (2001). Magic Graph, Birkhauser, Boston.

Wilson, R.J. (1996). Introduction to Graph Theory, Ed. 4. Mala: Longman.

Published
14-06-2023
How to Cite
Setiawati, J., Meryta Febrilian Fatimah, & Ekawati, D. (2023). Pelabelan Total Tak Reguler Sisi pada Graf Direction, Graf Direction Right, dan Graf Heart. Proximal: Jurnal Penelitian Matematika Dan Pendidikan Matematika, 6(2), 64-72. https://doi.org/10.30605/proximal.v6i2.2559
Issue
Vol. 6 No. 2 (2023): Matematika dan Pendidikan Matematika: Permasalahan dan Solusinya
Section
Articles

Copyright (c) 2023 JULI SETIAWATI, Meryta Febrilian Fatimah, DARMA EKAWATI

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