BILANGAN TERHUBUNG PELANGI PADA GRAF HASIL OPERASI KORONA GRAF ANTIPRISMA (APm) DAN GRAF LENGKAP (K4)
DOI:
https://doi.org/10.25077/jmua.11.2.112-123.2022Abstract
Bilangan terhubung pelangi didefinisikan sebagai banyaknya jumlah warna minimum yang dibutuhkan untuk membuat graf G menjadi terhubung pelangi, dengan syarat sisi yang termasuk dalam lintasan pelangi tidak boleh memiliki warna yang sama. Bilangan terhubung pelangi disimbolkan dengan rc(G). Seiring berkembangnya ilmu pengetahuan dan penelitian, maka bilangan terhubung pelangi mulai diterapkan ke dalam operasi graf. Penelitian ini menggunakan operasi korona untuk mengetahui bilangan terhubung pelangi dari graf antiprisma (APm) dan graf lengkap (K4). Berdasarkan hasil penelitian, maka diperoleh teorema bilangan terhubung pelangi dari graf (APm ⊙ K4) = 2m untuk 3 ≤ m ≤ 7 dan bilangan terhubung pelangi dari graf (K4 ⊙ APm) = 4 untuk m = {3, 4} ∧ 2m − 2 untuk 5 ≤ m ≤ 9, m ganjil ∧ 2m untuk 5 ≤ m ≤ 9, m genap.Downloads
References
Lestari, D., 2020, Bilangan Keterhubungan Pelangi pada Pewarnaan Sisi Graf, Jurnal Ilmiah Matematika, 8(1) : 25 – 34
Afriantini., Helmi., Fran, F., 2019, Pewarnaan Simpul, Sisi, Wilayah pada Graf dan Penerapannya, Bimaster Ilmiah. Stat. dan Terapannya, 8(4) : 773 – 782
Wijaya, R., 2013, Bilangan Rainbow Connection untuk Graf Komplemen, Jurnal Matematika UNAND, 2(3) : 19 – 12
Chartrand, G., Kalamazoo., Johns, G. L., Valley, S., Mckeon, K. A., London, N., Zhang, P., Kalamazoo., 2008, Rainbow Connection in Graphs, Mathematica Bohemica, 133(1) : 85 – 98
Harsya, A. Y., Agustin, I. H., Dafik., 2014, Pewarnaan Titik Pada Operasi Graf Sikel dengan Graf Lintasan, Jurnal Universitas Jember, 1(1) : 11 – 18
Hader, A. E., 2020, Bilangan Terhubung Pelangi pada Graf Korona Kipas dan Roda dengan Graf Trivial, Jurnal SIMTIKA, 3(1) : 31 – 34
Darmawan, R. N., Dafik., 2014, Rainbow Connection Number of Prism and Product of Two Graphs, Prosiding Seminar Nasional Matematika Jember, 1(1): 10 – 17
Ardiansyah, R., 2013, Bilangan Kromatik Graf Hasil Amalgamasi Dua Buah Graf, Jurnal Sains dan Seni POMITS, 2(1) : 1 – 5
Fitriani, F., Cahyaningtias, S., 2021, Graf Dual Antiprisma dan Dimensi Metriknya, E-Jurnal Matematika, 10(1) : 6 – 11
Wahyuni, Y., Utoyo, M. I., Slamin., 2019, Bilangan Dominasi Graf Hasil Operasi Korona Sisi, Limits: Journal of Mathematics and Its Applications, 16(2) : 135 – 146
Budayasa, I. K., 2021, Bilangan Keterhubungan Pelangi Graf â€Snark†Bunga, Jurnal Ilmiah Matematika, 09(01) : 89 – 95
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