Representasi Graf Pangkat Pada Grup Bilangan Bulat Modulo Berorde Bilangan Prima
Keywords:
graf pangkat, grup, bilangan bulat modulo
Abstract
Graf kini sangat menarik untuk dikaji karena pada beberapa tahun terakhir graf mulai digunakan untuk menggambarkan objek abstrak pada sistem bilangan, seperti pada grup dan gelanggang. Graf menghadirkan bentuk fisik dari suatu grup dengan relasi antar elemennya terlihat kasat mata. Akibatnya, jarak antar elemen pada grup juga memungkinkan untuk didefinisikan menggunakan karakteristik dari graf itu sendiri. Pada penelitian ini, penulis membahas tentang sifat-sifat graf pangkat pada grup bilangan bulat modulo yang berorder suatu bilangan prima. Metode yang digunakan dalam penelitian ini adalah deductive proof. Hasil yang didapatkan dari penelitian ini adalah graf pangkat dari grup bilangan bulat modulo yang berorde suatu bilangan prima adalah graf lengkap . Graf pangkat pada grup bilangan bulat modulo yang berorde suatu bilangan prima memiliki radius dan diameter yang sama, yaitu 1. Dan juga memiliki bilangan kromatik dan bilangan clique yang sama, yaitu n.References
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Syarifudin, A. G., Wardhana, I. G. A. W., Switrayni, N. W., & Aini, Q. (2021). The Clique Numbers and Chromatic Numbers of The Coprime Graph of a Dihedral Group. IOP Conference Series: Materials Science and Engineering, 1115(1), 012083. https://doi.org/10.1088/1757-899x/1115/1/012083
Aşkin, V., & Büyükköse, Ş. (2021). The Wiener Index of an Undirected Power Graph. Advances in Linear Algebra & Matrix Theory, 11(01), 21–29. https://doi.org/10.4236/alamt.2021.111003
Asmarani, E. Y., Syarifudin, A. G., Adhitya, G., Wardhana, W., & Switrayni, W. (2021). Eigen Mathematics Journal The Power Graph of a Dihedral Group. 4(2). https://doi.org/10.29303/emj.v4i2.117
Chelvam, T., & Sattanathan, M. (2013). Power graph of finite abelian groups. Algebra and Discrete Mathematics, 16(1), 33–41.
Husni, M. N., Syafitri, H., Siboro, A. M., Syarifudin, A. G., Aini, Q., & Wardhana, I. G. A. W. (2022). THE HARMONIC INDEX AND THE GUTMAN INDEX OF COPRIME GRAPH OF INTEGER GROUP MODULO WITH ORDER OF PRIME POWER. BAREKENG: Jurnal Ilmu Matematika Dan Terapan, 16(3), 961–966. https://doi.org/10.30598/barekengvol16iss3pp961-966
Juliana, R., Wardhana, I. G. A. W., & Irwansyah. (2021). Some Characteristics of Cyclic Prime, Weakly Prime and Almost Prime Submodule of Gaussian Integer Modulo over Integer. AIP Conference Proceedings, 2329(February). https://doi.org/10.1063/5.0042586
Ma, X., Wei, H., & Yang, L. (2014). The Coprime graph of a group. International Journal of Group Theory, 3(3), 13–23. https://doi.org/10.22108/ijgt.2014.4363
Mansoori, F., Erfanian, A., & Tolue, B. (2016). Non-coprime graph of a finite group. AIP Conference Proceedings, 1750(June 2016). https://doi.org/10.1063/1.4954605
Misuki, W. U., Wardhana, I. G. A. W., Switrayni, N. W., & Irwansyah. (2021). Some results of non-coprime graph of the dihedral group D2n for n a prime power. AIP Conference Proceedings, 2329(February). https://doi.org/10.1063/5.0042587
Nurhabibah, Malik, D. P., Syafitri, H., & Wardhana, I. G. A. W. (2022). Some results of the non-coprime graph of a generalized quaternion group for some n. 020001. https://doi.org/10.1063/5.0114975
Nurhabibah, N., Gazir Syarifudin, A., Gede Adhitya Wisnu Wardhana, I., & Aini, Q. (2021). Eigen Mathematics Journal The Intersection Graph of a Dihedral Group. 4(2). https://doi.org/10.29303/emj.v4i2.119
Nurhabibah, N., Syarifudin, A. G., & Wardhana, I. G. A. W. (2021). Some Results of The Coprime Graph of a Generalized Quaternion Group Q_4n. InPrime: Indonesian Journal of Pure and Applied Mathematics, 3(1), 29–33. https://doi.org/10.15408/inprime.v3i1.19670
Ramdani, D. S., Wardhana, I. G. A. W., & Awanis, Z. Y. (2022). THE INTERSECTION GRAPH REPRESENTATION OF A DIHEDRAL GROUP WITH PRIME ORDER AND ITS NUMERICAL INVARIANTS. BAREKENG: Jurnal Ilmu Matematika Dan Terapan, 16(3), 1013–1020. https://doi.org/10.30598/barekengvol16iss3pp1013-1020
Syarifudin, A. G., Nurhabibah, Malik, D. P., & dan Wardhana, I. G. A. W. (2021). Some characterizatsion of coprime graph of dihedral group D2n. Journal of Physics: Conference Series, 1722(1). https://doi.org/10.1088/1742-6596/1722/1/012051
Syarifudin, A. G., Wardhana, I. G. A. W., Switrayni, N. W., & Aini, Q. (2021). The Clique Numbers and Chromatic Numbers of The Coprime Graph of a Dihedral Group. IOP Conference Series: Materials Science and Engineering, 1115(1), 012083. https://doi.org/10.1088/1757-899x/1115/1/012083
Published
2022-12-31
Section
Articles
Copyright (c) 2022 Bulqis Nebulla Syechah, Evi Yuniartika Asmarani, Abdul Gazir Syarifudin, Dara Puspita Anggraeni, I Gede Adhitya Wisnu Wardhana
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