Bilangan Terhubung Pelangi Graf Garis dan Graf Tengah dari Graf Hasil Operasi Korona Graf Lintasan 〖(P〗_n) dan Lingkaran 〖(C〗_3)
DOI:
https://doi.org/10.31004/joecy.v6i2.8942Keywords:
Bilangan Terhubung Pelangi, Graf Tengah, Graf Lintasan, Graf Lingkaran, Operasi Korona, Rainbow Connection Number, Middle Graph, Path Graph, Cycle Graph, Corona OperationAbstract
This study discusses the determination of the rainbow connection number on middle graphs obtained from the corona product between a path graph and a cycle graph . The purpose of this research is to determine the value of the rainbow connection number of these graph structures and to examine their fundamental properties through a graph theory approach. The research method was conducted through a literature study by reviewing the basic concepts of graph theory, the corona operation, and the characteristics of line and middle graphs. The analysis was carried out by developing definitions, theorems, and proofs using an inductive approach. The results show that for the line graph of the corona product between the path graph and the cycle graph , the rainbow connection number is , where represents the diameter of the graph. This finding contributes to the development of the rainbow coloring concept in graph theory and may serve as a reference for future studies on total rainbow coloring and anti-magic rainbow coloring in other graph structures.
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Rumetna, M. S., Lina, T. N., Santoso, A. B., Komansilan, R., & Karay, J. (2023). Implementasi Algoritma Depth First Search Dalam Penyelesaian Permasalahan Lintasan dan Sirkuit Euler. Jurnal Komtika (Komputasi Dan Informatika), 7(1), 12–21. https://doi.org/10.31603/komtika.v7i1.8672
Setyorini, M. J. (2021). Bilangan Kromatik-b Graf Sentral, Tengah, dan Total dari Sebuah Bintang. MATHunesa: Jurnal Ilmiah Matematika, 9(1), 36–42.
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Welyanti, D., Andriani, N., & Yulianti, L. (2023). Bilangan Kromatik Lokasi Pada Graf Amalgamasi Kipas Berekor. Limits: Journal of Mathematics and Its Applications, 20(1), 81–95. https://doi.org/10.12962/limits.v20i1.12948
Afrianti, A., Helmi, H., & Fran, F. (2019). Pewarnaan simpul, sisi, wilayah pada graf dan penerapannya. Bimaster : Buletin Ilmiah Matematika, Statistika Dan Terapannya, 8(4), 773–782. https://doi.org/10.26418/bbimst.v8i4.36037
Bustan, A. W. (2017). BILANGAN TERHUBUNG PELANGI UNTUK GRAF OLEANDER (The Rainbow Connection Number of Oleander Graphs).
Chartrand, G., Johns, G. L., Mckeon, K. A., & Zhang, P. (2008). Mathematica Bohemica Terms of use : 133(1), 85–98.
Ginting, S. S. B., & Mulyono, M. (2023). Bilangan Kromatik Dari Graf Hasil Operasi Korona Pada Graf Bintang Dan Graf Ligkaran. Jurnal Riset Rumpun Matematika Dan Ilmu Pengetahuan Alam (JURRIMIPA), 2(2), 263–269. https://doi.org/10.55606/jurrimipa.v2i2.1622
Krivelevich, M., & Yuster, R. (2010). The rainbow connection of a graph is (at most) reciprocal to its minimum degree. Journal of Graph Theory, 63(3), 185–191. https://doi.org/10.1002/jgt.20418
Kumala, I. S. (2019). Bilangan Terhubung Pelangi Graf Bunga (W_m,K_n) dan Graf Lemon (Le_n). Jurnal Matematika Dan Pendidikan Matematika, 4(1), 39–48.
Li, X., & Sun, Y. (2011). Rainbow connection numbers of line graphs.
Lihawa, I., Ismail, S., Hasan, I. K., Yahya, L., Nasib, S. K., & Yahya, N. I. (2022). Bilangan Terhubung Titik Pelangi pada Graf Hasil Operasi Korona Graf Prisma (P_(m,2)) dan Graf Lintasan (P_3). Jambura Journal of Mathematics, 4(1), 145–151. https://doi.org/10.34312/jjom.v4i1.11826
Noor, C. A. P., Mamonto, K. A., & Pranata, W. E. (2019). Bilangan terhubung pelangi pada amalgamasi graf berlian. Euler : Jurnal Ilmiah Matematika, Sains Dan Teknologi, 7(1), 1–5. https://doi.org/10.34312/euler.v7i2.10345
Noor, C. A. P., Yahya, L., Nasib, S. K., & Yahya, N. I. (2021). BILANGAN TERHUBUNG PELANGI PADA GRAF SALJU (Sn_m). Journal of Fundamental Mathematics and Applications (JFMA), 4(1), 29–44. https://doi.org/10.14710/jfma.v4i1.9035
Rumetna, M. S., Lina, T. N., Santoso, A. B., Komansilan, R., & Karay, J. (2023). Implementasi Algoritma Depth First Search Dalam Penyelesaian Permasalahan Lintasan dan Sirkuit Euler. Jurnal Komtika (Komputasi Dan Informatika), 7(1), 12–21. https://doi.org/10.31603/komtika.v7i1.8672
Setyorini, M. J. (2021). Bilangan Kromatik-b Graf Sentral, Tengah, dan Total dari Sebuah Bintang. MATHunesa: Jurnal Ilmiah Matematika, 9(1), 36–42.
Vilgalita, B. G., Yundari, Y., & Fran, F. (2020). Bilangan terhubung titik pelangi pada graf kuadratik dan graf garis dari graf kembang api. Bimaster : Buletin Ilmiah Matematika, Statistika Dan Terapannya, 9(2), 343–350. https://doi.org/10.26418/bbimst.v9i2.40221
Welyanti, D., Andriani, N., & Yulianti, L. (2023). Bilangan Kromatik Lokasi Pada Graf Amalgamasi Kipas Berekor. Limits: Journal of Mathematics and Its Applications, 20(1), 81–95. https://doi.org/10.12962/limits.v20i1.12948
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