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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi JMPM: Jurnal Matematika dan Pendidikan Matematika EIGEN MATHEMATICS JOURNAL InPrime: Indonesian Journal Of Pure And Applied Mathematics JPIn : Jurnal Pendidik Indonesia International Journal of Research in Community Services Operations Research: International Conference Series International Journal of Global Operations Research Evolusi: Journal of Mathematics and Natural Sciences Journal of Fundamental Mathematics and Applications (JFMA)
Abdul Gazir Syarifudin
Universitas Kebangsaan Republik Indonesia
Agriculture, Biological Sciences & Forestry Biochemistry, Genetics & Molecular Biology Chemistry Computer Science & IT Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Energy Engineering Mathematics Social Sciences Other

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Journal : InPrime: Indonesian Journal Of Pure And Applied Mathematics

 1 
Some Results of The Coprime Graph of a Generalized Quaternion Group Q_4n Nurhabibah Nurhabibah; Abdul Gazir Syarifudin; I Gede Adhitya Wisnu Wardhana
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 3, No 1 (2021)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15408/inprime.v3i1.19670

Abstract

AbstractThe Coprime graph is a graph from a finite group that is defined based on the order of each element of the group. In this research, we determine the coprime graph of generalized quaternion group Q_(4n) and its properties. The method used is to study literature and analyze by finding patterns based on some examples. The first result of this research is the form of the coprime graph of a generalized quaternion group Q_(4n) when n = 2^k, n an odd prime number, n an odd composite number, and n an even composite number. The next result is that the total of a cycle contained in the coprime graph of a generalized quaternion group Q_(4n) and cycle multiplicity when  is an odd prime number is p-1.Keywords: Coprime graph, generalized quaternion group, order, path AbstrakGraf koprima merupakan graf dari dari suatu grup hingga yang didefiniskan berdasarkan orde dari masing-masing elemen grup tersebut. Pada penelitian ini akan dibahas tentang bentuk graf koprima dari grup generalized quaternion Q_(4n). Metode yang digunakan dalam penelitian ini adalah studi literatur dan melakukan analisis berdasarkan pola yang ditemukan dalam beberapa contoh. Adapun hasil pertama dari penelitian adalah bentuk graf koprima dari grup generalized quaternion Q_(4n) untuk kasus n = 2^k, n bilangan prima ganjil ganjil, n bilangan komposit ganjil dan n bilangan komposit genap. Hasil selanjutnya adalah total sikel pada graf koprima dari grup generalized quaternion dan multiplisitas sikel ketika  bilangan prima ganjil adalah p-1.Kata kunci: Graf koprima, grup generalized quternion, orde
Co-Authors Amelia, Rika Chairunnisa, Nadine Zahra Dara Purnamasari Dara Puspita Anggraeni Dewi, Putu Kartika Evi Yunartika Asmarani Evi Yuniartika Asmarani Evi Yuniartika Asmarani Hidayana, Rizki Apriva I Gede Adhitya Wisnu Wardhana Irwansyah Irwansyah Kholipah, Nenden Siti Nur Malik, Deny Putra Manuela, Angellyca Leoni Masriani Masriani Maulana, Fariz Megantara, Tubagus Robbi Nenden Siti Nurkholipah, Nenden Siti Ni Wayan Switrayni Nurhabibah Nurhabibah Nurhabibah Nurhabibah Qurratul Aini Rina Juliana Sahin Two Lestari Salwa Salwa Widiastuti, Ratna Sari Wijaya, Verrel Rievaldo Yuningsih, Siti Hadiaty Zata Yumni Awanis