Odd Harmonious Labeling of the Zinnia Flower Graphs
DOI:
https://doi.org/10.35799/jis.v23i1.46771Keywords:
flower graph, odd harmonious graph, odd harmonious labelling, zinnia flowerAbstract
An odd harmonious graph is a graph that satisfies the odd harmonious labeling properties. In this study, a new graph class construction is presented, namely zinnia flower graphs and variations of the zinnia flower graphs. The research method used is qualitative and includes several phases, namely data collection, data processing and analysis, and verification of the results. The purpose of this research is to find a new class of graphs that is a family of odd harmonious graphs. We will prove that prove that the zinnia flower graph and its variations satisfy odd harmonious labeling properties. The result of this research is that the zinnia flower graph and its variations are odd harmonious graphs.
Keywords: Flower graph; odd harmonious graph; odd harmonious labelling; zinnia flower graph
Pelabelan Harmonis Ganjil dari Graf Bunga Zinnia
ABSTRAK
Graf yang memiliki sifat pelabelan harmonis ganjil adalah graf harmonis ganjil. Pada penelitian ini akan didapatkan konstruksi graf bunga zinnia dan variasi graf bunga zinnia. Metode penelitian yang digunakan adalah penelitian kualitatif yang terdiri beberapa tahapan yaitu pengumpulan data, pengolahan dan analisis data, serta verifikasi hasil. Tujuan penelitian ini adalah menemukan kelas graf baru yang merupakan keluarga dari graf harmonis ganjil. Hasil penelitian ini diperoleh bahwa graf bunga zinnia dan variasi graf bunga zinnia merupakan graf harmonis ganjil.
Kata kunci: Graf bunga; graf bunga zinnia; graf harmonis ganjil; pelabelan harmonis ganjil
References
Abdel-Aal, M. E. (2013). Odd Harmonious Labelings of Cyclic Snakes. International Journal on Applications of Graph Theory In Wireless Ad Hoc Networks And Sensor Networks, 5(3), 1–11. https://doi.org/10.5121/jgraphoc.2013.5301.
Abdel-Aal, & Seoud. (2016). Further Results on Odd Harmonious Graphs. International Journal on Applications of Graph Theory In Wireless Ad Hoc Networks And Sensor Networks, 8(4), 1–14. https://doi.org/10.5121/jgraphoc.2016.8401.
Febriana, F., & Sugeng, K. A. (2020). Odd harmonious labeling on squid graph and double squid graph. Journal of Physics: Conference Series, 1538(1), 1–5. https://doi.org/10.1088/1742-6596/1538/1/012015.
Firmansah, F. (2017). The Odd Harmonious Labeling on Variation of the Double Quadrilateral Windmill Graphs. Jurnal Ilmu Dasar, 18(2), 109-118. https://doi.org/10.19184/jid.v18i2.5648.
Firmansah, F. (2020a). Pelabelan Harmonis Ganjil pada Graf Bunga Double Quadrilateral. Jurnal Ilmiah Sains, 20(1), 12–17. https://doi.org/10.35799/jis.20.1.2020.27278.
Firmansah, F. (2020b). Pelabelan Harmonis Ganjil pada Graf Ular Jaring Berlipat. Sainmatika: Jurnal Ilmiah Matematika Dan Ilmu Pengetahuan Alam, 17(1), 1–8. https://doi.org/10.31851/sainmatika.v17i1.3182.
Firmansah, F. (2022). Odd Harmonious Labeling on Some String Graph Classes. BAREKENG: Jurnal Ilmu Matematika Dan Terapan, 16(1), 315-322. https://doi.org/10.30598/barekengvol16iss1pp313-320.
Firmansah, F. (2023). The Odd Harmonious Labeling of Layered Graphs. JTAM (Jurnal Teori Dan Aplikasi Matematika), 7(2), 339–348. https://doi.org/ 10.31764/jtam.v7i2.12506.
Firmansah, F., & Giyarti, W. (2021). Odd harmonious labeling on the amalgamation of the generalized double quadrilateral windmill graph. Desimal: Jurnal Matematika, 4(3), 373–378. https://doi.org/10.24042/djm.
Firmansah, F., & Tasari. (2020). Odd Harmonious Labeling on Edge Amalgamation from Double Quadrilateral Graphs. Desimal: Jurnal Matematika, 3(1), 65–72. https://doi.org/10.24042/djm.v3i1.5712.
Firmansah, F., & Yuwono, M. R. (2017a). Pelabelan Harmonis Ganjil pada Kelas Graf Baru Hasil Operasi Cartesian Product. Jurnal Matematika Mantik, 03(02), 87–95. https://doi.org/10.15642/mantik.2017.3.2.87-95.
Firmansah, F., & Yuwono, M. R. (2017b). Odd Harmonious Labeling on Pleated of the Dutch Windmill Graphs. CAUCHY, 4(4), 161. https://doi.org/10.18860/ca.v4i4.4043
Gallian, J. A. (2022). A Dynamic Survey of Graph Labeling. The Electronic Journal of Combinatorics, 25, 127–133.
Jeyanthi, P., & Philo, S. (2019). Some Results On Odd Harmonious Labeling Of Graphs. Bulletin Of The International Mathematical Virtual Institute, 9, 567–576. https://doi.org/10.7251/BIMVI1903567J.
Jeyanthi, P., Philo, S., & Sugeng, K. A. (2015). Odd harmonious labeling of some new families of graphs. SUT Journal of Mathematics, 51(2), 181–193. https://doi.org/10.1016/j.endm.2015.05.024.
Liang, Z. H., & Bai, Z. L. (2009). On the odd harmonious graphs with applications. Journal of Applied Mathematics and Computing, 29(1–2), 105–116. https://doi.org/10.1007/s12190-008-0101-0.
Philo, S., & Jeyanthi, P. (2021). Odd Harmonious Labeling of Line and Disjoint Union of Graphs. Chinese Journal of Mathematical Sciences, 1(1), 61–68.
Sarasvati, S. S., Halikin, I., & Wijaya, K. (2021). Odd Harmonious Labeling of Pn C4 and Pn D2(C4). Indonesian Journal of Combinatorics, 5(2), 94–101. https://doi.org/10.19184/ijc.2021.5.2.5.
Seoud, M. A. A., & Hafez, H. M. (2018). Odd harmonious and strongly odd harmonious graphs. Kyungpook Mathematical Journal, 58(4), 747–759. https://doi.org/10.5666/KMJ.2018.58.4.747.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 Fery Firmansah, Tasari Tasari, Muhammad Ridlo Yuwono
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
LICENCE: CC-BY-NC
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License
