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All Journal JURNAL MATEMATIKA STATISTIKA DAN KOMPUTASI CAUCHY: Jurnal Matematika Murni dan Aplikasi Journal of the Indonesian Mathematical Society Jurnal Matematika & Sains JMPM: Jurnal Matematika dan Pendidikan Matematika BAREKENG: Jurnal Ilmu Matematika dan Terapan Unisda Journal of Mathematics and Computer Science (UJMC) JTAM (Jurnal Teori dan Aplikasi Matematika) Beta: Jurnal Tadris Matematika EIGEN MATHEMATICS JOURNAL Jurnal Abdi Insani Contemporary Mathematics and Applications (ConMathA) InPrime: Indonesian Journal Of Pure And Applied Mathematics JPIn : Jurnal Pendidik Indonesia Majalah Ilmiah Matematika dan Statistika (MIMS) Jurnal Ilmiah Abdi Mas TPB Unram Jurnal Diferensial Griya Journal of Mathematics Education and Application Evolusi: Journal of Mathematics and Natural Sciences Prosiding Konferensi Nasional PKM-CSR Journal of Fundamental Mathematics and Applications (JFMA) Jurnal Pepadu Basis : Jurnal Ilmiah Matematika Jurnal Pengabdian Inovasi Masyarakat Indonesia Pemberdayaan Masyarakat: Jurnal Aksi Sosial Sinergi dan Harmoni Masyarakat MIPA
I Gede Adhitya Wisnu Wardhana
Department Of Mathematics, Faculty Of Mathematics And Natural Science, University Of Mataram
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TOPOLOGY INDEX OF THE COPRIME GRAPH FOR DIHEDRAL GROUP OF PRIME POWER ORDER Marena Rahayu Gayatri; Rifdah Fadhilah; Sahin Two Lestari; Lia Fitta Pratiwi; Abdurahim Abdurahim; I Gede Adhitya Wisnu Wardhana
JURNAL DIFERENSIAL Vol 5 No 2 (2023): November 2023
Publisher : Program Studi Matematika, Universitas Nusa Cendana

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35508/jd.v5i2.12462

Abstract

In the field of molecular chemistry, graph theory is utilized to represent the structure of a molecule, where the set of nodes corresponds to its chemical elements and the set of edges represents the bonds within the chemical molecule. Graph theory, a mathematical discipline, finds application in various domains, one of which is group representation. This research will delve into the topic of the topological indices of the coprime graph of dihedral groups. The methodology employed involves reviewing several references related to dihedral groups, coprime graphs, and topological indices. This study yields results in the form of Harmonic index, Harary index, first Zagreb index, Gutman index, and Wiener index.
Numerical Invariants of Coprime Graph of A Generalized Quaternion Group Nurhabibah Nurhabibah; I Gede Adhitya Wisnu Wardhana; Ni Wayan Switrayni
Journal of the Indonesian Mathematical Society VOLUME 29 NUMBER 1 (MARCH 2023)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.29.1.1245.36-44

Abstract

The coprime graph of a finite group was defined by Ma, denoted by ΓG, is a graph with vertices that are all elements of group G and two distinct vertices x and y are adjacent if and only if (|x|, |y|) = 1. In this study, we discuss numerical invariants of a generalized quaternion group. The numerical invariant is a property of a graph in numerical value and that value is always the same on an isomorphic graph. This research is fundamental research and analysis based on patterns in some examples. Some results of this research are the independence number of ΓQ4n is 4n − 1 or 3n and its complement metric dimension is 4n − 2 for each n ≥ 2.
A Note on Free Module Decomposition over A Principal Ideal Domain Ni Wayan Switrayni; I Gede Adhitya Wisnu Wisnu Wardhana; Qurratul Aini
Journal of the Indonesian Mathematical Society VOLUME 29 NUMBER 2 (JULY 2023)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.29.2.1246.150-155

Abstract

Some methods have been used to express a finitely generated module over a principal ideal domain as a finite direct sum of its cyclic submodules. In this paper, we give an alternative technique to decompose a free module with finite rank over a principal ideal domain using eigen spaces of its endomorphism ring.
The Characterization of Almost Prime Submodule on the Finitely Generated Module over Principal Ideal Domain I Gede Adhitya Wisnu Wardhana; Pudji Astuti; Intan Muchtadi-Alamsyah
Journal of the Indonesian Mathematical Society VOLUME 30 NUMBER 1 (MARCH 2024)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.30.1.1396.63-76

Abstract

In most cases, almost prime submodules are equivalent to prime submodules, but in a finitely generated module, it is not necessarily equivalent. Based on the fact that a finitely generated module over a principal ideal domain can be decomposed into a free part and a torsion part, we give a new approach to the characteristic of almost prime submodules in the finitely generated module, especially we point out the cases when the submodules are almost prime but not prime.
Indeks Szeged dan Indeks Padmakar-Ivan pada Graf Nilpoten pada Gelanggang Bilangan Bulat Modulo Orde Prima Berpangkat Muhammad Naoval Husni; I Gede Adhitya Wisnu Wardhana; Putu Kartika Dewi; I Nengah Suparta
Jurnal Matematika, Statistika dan Komputasi Vol. 20 No. 2 (2024): JANUARY 2024
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/j.v20i2.31418

Abstract

Recently, graphs have started to be used to represent a finite ring. Nikmehr and  Khojasteh in the article  defined the nilpotent graph of a ring . Denoted , is a graph with the set of vertices being all the elements in the ring  Two vertices  and  are adjacent if and only if  is nilpotent elements in the ring . Topological index is a field that discusses graph structure based on the degree of each vertex of a graph and the distance between vertices.  In this study, the author will gives the general formula of the Szeged index and Padmakar-Ivan index of the nilpotent graph graph of the modulo ring with prime power order. The result of this research is a general formula for the topological indices of nilpotent graphs of the integer modulo ring, called the Szeged index and the Padmakar-Ivan index.
Penerapan Teori Permainan Dalam Menentukan Strategi Optimal Kemenangan Calon Presiden Dan Wakil Presiden Pada Ajang Pemilu 2024 M Fauzul; Ayes Malona Siboro; Putri Kurnia Chairunnisa; I Gede Adhitya Wisnu Wardhana; Baiq Rika Ayu Febrilia
Jurnal Matematika, Statistika dan Komputasi Vol. 20 No. 3 (2024): May 2024
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/j.v20i3.33285

Abstract

Game theory is applied in the context of the 2024 general election to determine effective strategies for each pair of candidates (paslon) presidential and vice presidential in the competition. This research yields several significant findings. In the match between paslon 1 and paslon 2, paslon 2 successfully secured victory with a score of -18, employing an optimal strategy focused on (candidate experience). Conversely, paslon 1 emerged victorious against paslon 3 with a score of 20, utilizing an optimal strategy based on (candidate vision and mission). In the final match between paslon 2 and paslon 3, paslon 2 once again achieved victory with a score of 36.88889. The optimal strategy for paslon 2 includes (candidate character), (candidate vision and mission), and (candidate experience). Paslon 3 also adopts a similar strategy. The results of this research provide insights into the development of candidate campaign strategies in the political competition context using a game theory approach.
THE CHEMICAL TOPOLOGICAL GRAPH ASSOCIATED WITH THE NILPOTENT GRAPH OF A MODULO RING OF PRIME POWER ORDER Malik, Deny Putra; Husni, Muhammad Naoval; Miftahurrahman, Miftahurrahman; Wardhana, I Gede Adhitya Wisnu; Semil @ Ismail, Ghazali
Journal of Fundamental Mathematics and Applications (JFMA) Vol 7, No 1 (2024)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v0i0.20269

Abstract

Chemical topological graph theory constitutes a subdomain within mathematical chemistry that leverages graph theory to model chemical molecules.  In this context, a chemical graph serves as a graphical representation of molecular structures. Specifically, a chemical molecule is portrayed as a graph wherein atoms are denoted as vertices, and the interatomic bonds are represented as edges within the graph. Various molecular properties are intricately linked to the topological indices of these molecular graphs. Notably, commonly employed indices encompass the Wiener Index, the Gutman Index, and the Zagreb Index.  This study is directed towards elucidating the numerical invariance and topological indices inherent to a nilpotent graph originating from a modulo integer ring with prime order. Consequently, the investigation seeks to discern how the Wiener Index, the Zagreb Index, and other characteristics of the nilpotent graph manifest within a ring of integers modulo prime order powers.
Indeks Padmakar-Ivan dan indeks Randic pada graf non-koprima dari grup bilangan bulat modulo Ghoffari, Lalu Hasan; Wardhana, I Gede Adhitya Wisnu; Abdurahim, Abdurahim
Majalah Ilmiah Matematika dan Statistika Vol 24 No 1 (2024): Majalah Ilmiah Matematika dan Statistika
Publisher : Jurusan Matematika FMIPA Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/mims.v24i1.45367

Abstract

Graph theory, introduced by the Swiss mathematician Leonhard Euler in 1736, has played a pivotal role in solving real-world problems since its inception, notably exemplified by Euler's solution to the Konigsberg Bridge problem. Its applications extend to various domains, including scheduling, shortest path routing, and chemical structure representation. In chemistry, graphs are extensively used to depict molecular structures and chemical compounds, aiding in visualizing atomic connections and overall compound configurations. Topology indices, such as the Padmakar-Ivan (PI) and Randic indices, provide numerical values capturing chemical bonding relationships. Beyond chemical structures, these indices find applications in abstract algebraic graph representations. Recent research, exemplified by Husni et al.'s work on the harmonic and Gutman indices, explores these indices in coprime graphs of integer groups modulo prime power orders. Additionally, studies on non-coprime graphs of integer groups modulo reveal unique characteristics and invariants, shedding light on their structure. The non-coprime graph is a graph with two vertices said to be adjacent if the greatest common divisor (GCD) of their orders is not equal to one. This paper aims to investigate the topological indices, specifically the Padmakar-Ivan and Randic indices, in non-coprime graphs of integer groups modulo, adding depth to our understanding of their applicability and significance in abstract algebraic representations. Keywords: Graph theory, padmakar-ivan index, randic index, non-coprime graphsMSC2020: 05C09
The First Zagreb Index, The Wiener Index, and The Gutman Index of The Power of Dihedral Group Asmarani, Evi Yuniartika; Lestari, Sahin Two; Purnamasari, Dara; Syarifudin, Abdul Gazir; Salwa, Salwa; Wardhana, I Gede Adhitya Wisnu
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 .
Some Results of The Coprime Graph of a Generalized Quaternion Group Q_4n Nurhabibah, Nurhabibah; Syarifudin, Abdul Gazir; Wardhana, I Gede Adhitya Wisnu
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 A.A. Ketut Agung Cahyawan W Abdul Gazir Syarifudin Abdurahim, Abdurahim Adelia Adelia Aenan Salsabila Afdhaluzzikri, M. Albaracin, Jimboy R. Alimon, Nur Idayu Ambar, Jinan Angamuthu, Manimaran Anisa Agustina Arzaki Zaget Oasis Asmarani, Evi Yuniartika Awanis, Zatta Yumni Ayes Malona Siboro Ayes Malona Siboro Ayes Malona Siboro Baiq Desy Aniska Prayanti Baiq Rika Ayu Febrilia Beni Nungroho Sudiantoro Biswas, Hena Rani Borisman Bertinegara Dara Purnamasari Dara Puspita Anggraeni Devia Arisanti Dewi, Putu Kartika Dina Eka Putri Dwi Noorma Putri Evi Yunartika Asmarani Evi Yuniartika Asmarani Evi Yuniartika Asmarani Evi Yuniartika Asmarani Fathul Maulina Wahidah Febrilia, Baiq Rika Ayu Gambo, Ibrahim Ghazali Semil @ Ismail Ghoffari, Lalu Hasan Hijriati, Naimah Hisan, Khairatun Husni, Muhammad Naoval Ida Rohani Ilham Ilham Intan Muchtadi-Alamsyah Irwansyah Irwansyah Irwansyah Irwansyah Jurnal Pepadu Karang, Gusti Yogananda Laila Hayati Lailia Awalushaumi Lalu Hasan Ghoffari Lalu Riski Wirendra Putra Lalu Riski Wirendra Putra Lestari, Sahin Two Lia Fitta Pratiwi M Fauzul M. Afdhol Gilman Malik, Deny Putra MAMIKA UJIANITA ROMDHINI Mamika Ujianita Romdhini Mamika Ujianita Romdhini, Mamika Ujianita Marena Rahayu Gayatri Marena Rahayu Gayatri Masriani Masriani Masriani Masriani Maulana, Fariz MAXRIZAL Miftahurrahman, Miftahurrahman Muhammad Naoval Husni Muhammad Rijal Alfian Muklas Maulana Munawara Putia Ni Wayan Switrayni Ni Wayan Switrayni Ni Wayan Switrayni Nur Asmita Purnamasari Nurhabibah Nurhabibah Nurhabibah Nurhabibah Nurhabibah Nurhabibah Nurhabibah Nurhabibah Nuzla Af'idatur Robbaniyyah Pratama, Rendi Bahtiar Prof. Dr.I Nengah Suparta,M.Si . Pudji Astuti Purnamasari, Dara Putra, Lalu Riski Wirendra Putri Kurnia Chairunnisa Putu Kartika Dewi Qurratul Aini Qurratul Aini Qurratul Aini Ramdani, Dewi Santri Rendi Bahtiar Pratama Rifdah Fadhilah Rina Juliana Rina Juliana Sahin Two Lestari Sahin Two Lestari Salwa Salwa Salwa Salwa Salwa Salwa Salwa Salwa Salwa Salwa Salwa Salwa Sarmin, Nor Haniza Satriawan, Didit Semil @ Ismail, Ghazali Siboro, Ayes Malona Siti Raudhatul Kamali Surya Hadi Syafitri, Hanna Syaftirridho Putri Ubaidillah, Moch Rafi Zarkasy Widiastuti, Ratna Sari Yatin, Bela Zainun Zata Yumni Awanis Zata Yumni Awanis Zata Yumni Awaris