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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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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
SUBGRUP DARI GRUP TORSI YANG DIBANGUN SECARA HINGGA PADA C* Abdul Gazir S; I Gede Adhitya Wisnu Wardhana; Ni Wayan Switrayni; Qurratul Aini
Jurnal Pendidik Indonesia (JPIn) Vol 2, No 1: April 2019
Publisher : Yayasan Pendidikan Intan Cendekia

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.47165/jpin.v2i1.66

Abstract

Grup adalah sebuah pasangan terurut pada sebuah himpunan tak kosong yang memenuhi sifat asosiatif, memiliki invers dan identitas. Grup torsi adalah suatu grup yang setiap elemennya berorde hingga. Grup torsi erat kaitanya dengan grup siklik, bagaimana hubungan keduanya, apakah unsur grup torsi pada C* dan apa pembangun dari C* akan dibahas  dalam makalah ini..
Subgrup Non Trivial Dari Grup Dihedral Abdul Gazir; I Gede Adhitya Wisnu Wardhana
Eigen Mathematics Journal Vol. 2 No. 2 Desember 2019
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v1i2.26

Abstract

Grup  dikatakan grup dihedral dengan order , adalah grup yang dibangun oleh dua elemen  dengan sifat . Grup dihedral dinotasikan dengan .  Sama halnya dengan grup yang lain, grup dihedral juga memiliki subgrup. Pada paper ini akan dibahas teorema-teorema yang berkaitan dengan subgrup dihedral, adapun salah satunya hasilnya dapat memperlihatkan jika  prima maka subgrup-subgrup dibagi kedalam 2 macam yaitu subgrup yang mengandung rotasi dan subgrup yang mengandung refleksi sedangkan jika  komposit maka subgrup-subgrupnya dibagi kedalam 3 macam subgrup yaitu subgrup yang mengandung rotasi, refleksi dan gabungannya.
Some Special Graphs of Quaternion Group Abdul Gazir S; I Gede Adhitya Wisnu Wardhana
Eigen Mathematics Journal Vol. 4 No. 1 Juni 2021
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v4i1.74

Abstract

Research on an algebraic structure represented in graph theory opens the way for new research in recent years. Several types of new graphs continue to be developed, such as coprime and non-coprime graphs. This article will represent the quaternion group in several graphs, such as coprime graphs, non-coprime graphs, commuting graphs, non-commuting graphs, and identity graphs. We obtained several theorems about unique graphs. One of the results is that non-coprime graphs from the quaternion group are complete and regular graphs.
The Power Graph of a Dihedral Group Evi Yunartika Asmarani; Abdul Gazir Syarifudin; I Gede Adhitya Wisnu Wardhana; Ni Wayan Switrayni
Eigen Mathematics Journal Vol. 4 No. 2 Desember 2021
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v4i2.117

Abstract

Graph theory is one of the topics in mathematics that is quite interesting to study because it is applicable and can be combined with other mathematical topics such as group theory. The combination of graph theory and group theory is that graphs can be used to represent a group. An example of a graph is a power graph. A power graph of the group  is defined as a graph whose vertex set is all elements of  and two distinct vertices  and  are connected if and only if  or for a positive integer x and y. In this study, the author discusses the power graph of the dihedral group  The results obtained from this study are the power graph of the dihedral group  where  with  prime numbers and an  natural number is a graph consisting of two non-disjoint subgraphs, namely complete subgraphs and star subgraphs. And we find that its radius and diameter are 1 and 2.
The Intersection Graph of a Dihedral Group Nurhabibah Nurhabibah; Abdul Gazir Syarifudin; I Gede Adhitya Wisnu Wardhana; Qurratul Aini
Eigen Mathematics Journal Vol. 4 No. 2 Desember 2021
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v4i2.119

Abstract

The intersection graph of a finite group G is a graph (V,E) where V is a set of all non-trivial subgroups of G and E is a set of edges where two distinct subgroups H_i , H_j  are said to be adjacent if and only if H_i \cap H_j \neq {e} . This study discusses the intersection graph of a dihedral group D_{2n} specifically the subgraph, degree of vertices, radius, diameter, girth, and domination number. From this study, we obtained that if n=p^2 then the intersection graph of D_{2n} is containing complete subgraph K_{p+2} and \gamma(\Gamma_{D_{2n}})=p. 
SOME RESULT OF NON-COPRIME GRAPH OF INTEGERS MODULO n GROUP FOR n A PRIME POWER Masriani Masriani; Rina Juliana; Abdul Gazir Syarifudin; I Gede Adhitya Wisnu Wardhana; Irwansyah Irwansyah; Ni Wayan Switrayni
Journal of Fundamental Mathematics and Applications (JFMA) Vol 3, No 2 (2020)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (275.367 KB) | DOI: 10.14710/jfma.v3i2.8713

Abstract

One interesting topic in algebra and graph theory is a graph representation of a group, especially the representation of a group using a non-coprime graph.  In this paper, we describe the non-coprime graph of integers modulo  group and its subgroups, for  is a prime power or  is a product of two distinct primes.
SOME PROPERTIES OF COPRIME GRAPH OF DIHEDRAL GROUP D_2n WHEN n IS A PRIME POWER Abdul Gazir S; I Gede Adhitya Wisnu Wardhana; Ni Wayan Switrayni; Qurratul Aini
Journal of Fundamental Mathematics and Applications (JFMA) Vol 3, No 1 (2020)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (908.66 KB) | DOI: 10.14710/jfma.v3i1.7413

Abstract

The Study of algebraic structures, especially on graphs theory, leads to anew topics of research in recent years. In this paper, the algebraic structures that will be represented by a coprime graph are the dihedral group and its subgroups. The coprime graph of a group G, denoted by \Gamma_D_2n is a graph whose vertices are elements of G and two distinct vertices a and b are adjacent if only if (|a,|b|)=1. Some properties of the coprime graph of a dihedral group D_2n are obtained. One of the results is if n is prime then \Gamma_D_2n is a complete bipartite graph. Moreover, if n is the power of prime then \Gamma_D_2n is a multipartite graph.
Representasi Graf Pangkat Pada Grup Bilangan Bulat Modulo Berorde Bilangan Prima Bulqis Nebulla Syechah; Evi Yuniartika Asmarani; Abdul Gazir Syarifudin; Dara Puspita Anggraeni; I Gede Adhitya Wisnu Wardhana
EVOLUSI: JOURNAL OF MATHEMATICS AND SCIENCES Vol 6 No 2 (2022): Oktober 2022
Publisher : Fakultas MIPA Universitas Nahdlatul Wathan Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.51673/evolusi.v6i2.1304

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.
The First Zagreb Index, The Wiener Index, and The Gutman Index of The Power of Dihedral Group Evi Yuniartika Asmarani; Sahin Two Lestari; Dara Purnamasari; Abdul Gazir Syarifudin; Salwa Salwa; I Gede Adhitya Wisnu Wardhana
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 7, No 4 (2023): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v7i4.16991

Abstract

Research on graphs combined with groups is an interesting topic in the field of combinatoric algebra where graphs are used to represent a group. One type of graph representation of a group is a power graph. A power graph of the group G is defined as a graph whose vertex set is all elements of G and two distinct vertices a and b are adjacent if and only if  or  for a positive integer  and . In addition to mathematics, graph theory can be applied to various fields of science, one of which is chemistry, which is related to topological indices. In this study, the topological indexes will be discussed, namely the Zagreb index, the Wiener index, and the Gutman index of the power graph of the dihedral group  where  with  prime numbers and an  natural number. The method used in this research is a literature review. The results obtained from this study are the first Zagreb index, Wiener index, and Gutman index of the power graph of the dihedral group  where  where  is prime and an m natural number respectively is .
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