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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 Mandalika Mathematics and Educations Journal 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 MATHunesa: Jurnal Ilmiah Matematika 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
Religion Agriculture, Biological Sciences & Forestry Humanities Biochemistry, Genetics & Molecular Biology Chemistry Civil Engineering, Building, Construction & Architecture Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Energy Engineering Environmental Science Health Professions Languange, Linguistic, Communication & Media Law, Crime, Criminology & Criminal Justice Materials Science & Nanotechnology Mathematics Mechanical Engineering Nursing Physics Public Health Social Sciences Transportation Other

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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
Molecular Topology Index of a Zero Divisor Graph on a Ring of Integers Modulo Prime Power Order Satriawan, Didit; Aini, Qurratul; Abdurahim; Maulana, Fariz; Wardhana, I Gede Adhitya Wisnu
Contemporary Mathematics and Applications (ConMathA) Vol. 6 No. 2 (2024)
Publisher : Universitas Airlangga

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20473/conmatha.v6i2.54737

Abstract

In chemistry, graph theory has been widely utilized to address molecular problems, with numerous applications in graph theory and ring theory within this field. One of these applications involves topological indices that represent chemical structures with numerical values. Various types of topological indices exist, including the Wiener index, the first Zagreb index, and the hyper-Wiener index. In the context of this research, the values of the Wiener index, the first Zagreb index, and the hyper-Wiener index for zero-divisor graphs on the ring of integers modulo a prime power order will be explored through a literature review and conjecture.
SOMBOR INDEX AND ITS GENERALIZATION OF POWER GRAPH OF SOME GROUP WITH PRIME POWER ORDER Pratama, Rendi Bahtiar; Maulana, Fariz; Hijriati, Na'imah; Wardhana, I Gede Adhitya Wisnu
Journal of Fundamental Mathematics and Applications (JFMA) Vol 7, No 2 (2024)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v7i2.22552

Abstract

Graphs are an intriguing topic of discussion due to their numerous applications, particularly in chemistry. Topological indices derived from graph representations of molecules enable us to predict various properties of these compounds, including their physical characteristics, chemical reactivity, biological activity, toxicity, and atom-to-atom interactions. More recently, graphs have also been utilized to depict abstract mathematical objects such as groups. A notable example of graph representation in group theory is seen in power graphs. This research explores new graph topological indices based on vertex degrees, inspired by the Euclidean metric, particularly the Sombor index, and its application to the power graph of the integer modulo group and the dihedral group. The primary outcome of this study is the derivation of a general formula for the Sombor index and its generalization.
Graf Nilpoten Dari Gelanggang Bilangan Bulat Modulo Berorde Pangkat Prima Malik, Deny Putra; Wardhana, I Gede Adhitya Wisnu; Dewi, Putu Kartika; Widiastuti, Ratna Sari; Maulana, Fariz; Syarifudin, Abdul Gazir; Awanis, Zata Yumni
JMPM: Jurnal Matematika dan Pendidikan Matematika Vol 8 No 1 (2023): March - August 2023
Publisher : Prodi Pendidikan Matematika Universitas Pesantren Tinggi Darul Ulum Jombang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26594/jmpm.v8i1.2920

Abstract

Nilpotent graph of ring integer modulo is one of the graph representations in algebraic structures. This study aims to find out the shape and properties of a nilpotent graph of ring prime numbers modulo which is then generalized to a ring of integers modulo with arbitrary prime power. The method used in this research is a literature study. In the ring of integer modulo, we get the shape of a nilpotent graph as a star graph. Then, the characteristic of a nilpotent graph on a ring integer modulo with arbitrary prime power is that it contains a complete subgraph and contains a number of as a star subgraph.
Hyper-Wiener and Szeged Indices of non-Coprime Graphs of Modulo Integer Groups Ghoffari, Lalu Hasan; Wardhana, I Gede Adhitya Wisnu; Dewi, Putu Kartika; Suparta, I Nengah
Eigen Mathematics Journal Vol 8 No 1 (2025): June
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v8i1.244

Abstract

The non-coprime graph of the integer modulo group is a graph whose vertices represent the elements of the integer modulo group, excluding the identity element. Two distinct vertices are adjacent if and only if their orders are not relatively prime. This study explores two topological indices, the Hyper-Wiener index and the Szeged index, in the non-coprime graph of the integer modulo-n group. The results reveal that these indices are equal when the order is a prime power but differ when the order is the product of two distinct prime numbers. This research provides new insights into the patterns and characteristics of these indices, contributing to a broader understanding of the application of graph theory to abstract group structures.
Algebraic Structures and Combinatorial Properties of Unit Graphs in Rings of Integer Modulo with Specific Orders Lestari, Sahin Two; Dewi, Putu Kartika; Wardhana, I Gede Adhitya Wisnu; Suparta, I Nengah
Eigen Mathematics Journal Vol 7 No 2 (2024): December
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v7i2.235

Abstract

Unit graph is the intersection of graph theory and algebraic structure, which can be seen from the unit graph representing the ring modulo n in graph form. Let R be a ring with nonzero identity. The unit graph of R, denoted by G(R), has its set of vertices equal to the set of all elements of R; distinct vertices x and y are adjacent if and only if x + y is a unit of R. In this study, the unit graph, which is in the ring of integers modulo n, denoted by G(Zn). It turns out when n is 2^k, G(Zn) forms a complete bipartite graph for k∈N, whereas when n is prime, G(Zn) forms a complete (n+1)/2-partites graph. Additionally, the numerical invariants of the graph G(Zn), such as degree, chromatic number, clique number, radius, diameter, domination number, and independence number complement the characteristics of G(Zn) for further research.
Co-Authors @ Ismail, Ghazali Semil A.A. Ketut Agung Cahyawan W Abdul Gazir Syarifudin Abdullah, Umar Abdurahim, Abdurahim Ade Candra, Ade Adelia Adelia Adelia Adelia, Adelia Aenan Salsabila Afdhaluzzikri, M. Ahmadil Hamdi Albaracin, Jimboy R. Alimon, Nur Idayu Ambar, Jinan Angamuthu, Manimaran Anisa Agustina Anisa Agustina, Anisa Apriliana, Haeva Ardana, Alfian Putra Arisanti, Devia Arzaki Zaget Oasis Asmarani, Evi Yuniartika Aulia, Sita Armi 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 Elfiyanti, Gustina Emmy Yuanita Evi Yunartika Asmarani Evi Yuniartika Asmarani Evi Yuniartika Asmarani Evi Yuniartika Asmarani Fadhilah, Rifdah Farwan, Farwan Fathul Maulina Wahidah Febrilia, Baiq Rika Ayu Gambo, Ibrahim Gayatri, Marena Rahayu Ghazali Semil @ Ismail Ghoffari, Lalu Hasan Gilman, M. Afdhol Graha, Syifa Salsabila Satya Hapsari, Mufidatul Ghina Haryati, Ida Hidayat, Muhammad Ahsan Hijriati, Naimah Hisan, Khairatun Husni, Muhammad Naoval Ida Rohani Ilham Ilham Ilham Ilham Indrawadi, Dimas Intan Muchtadi Alamsyah Intan Nadilah 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, Dia Lestari, Sahin Two Luzianawati, Luzianawati M Fauzul M. Afdhol Gilman Ma'wa, Jannatul Malik, Deny Putra MAMIKA UJIANITA ROMDHINI Mamika Ujianita Romdhini Mamika Ujianita Romdhini, Mamika Ujianita Maria Ulfa Masriani Masriani Masriani Masriani Maulana, Fariz Maulana, Muklas Maulani Rizqi Maulida Septiyana MAXRIZAL Miftahurrahman, Miftahurrahman Misuki, Wahyu Ulyafandhie Mufarrihati, Ardelia Muhammad Naoval Husni Muhammad Rijal Alfian Muklas Maulana Munawara Putia Musyarrofah, Sefti Fajriatul Nghiem, Nguyen Dang Hoa Ni Wayan Switrayni Ni Wayan Switrayni Ni Wayan Switrayni Nikken Prima Puspita Ningsih, Baiq Nila Sari Nur Asmita Purnamasari Nurhabibah Nurhabibah Nurhabibah Nurhabibah Nurhabibah Nurhabibah Nuzla Af'idatur Robbaniyyah Oasis, Arzaki Zaget Pradana, Satriawan Pratama, Rendi Bahtiar Pratiwi, Lia Fitta Prof. Dr.I Nengah Suparta,M.Si . PUDJI ASTUTI Purnamasari, Dara Putia, Munawara Putra, Lalu Riski Wirendra Putri Kurnia Chairunnisa Putri, Syaftirridho Putu Kartika Dewi Qudrani , Rabbelia Tri Qudrani, Rabbelia Qurratul Aini Qurratul Aini Qurratul Aini Ramdani, Dewi Santri Rendi Bahtiar Pratama Rina Juliana Rina Juliana Rio Satriyantara Robbaniyyah, Nuzla Af’idatur Rohani, Ida Rohiana, Siti Indah Sabil, M. Ibnu Sahin Two Lestari Sahin Two Lestari Salsabila, Aenan Salwa Salwa Salwa Salwa Salwa Salwa Salwa Salwa Salwa Salwa Santi, Laila Maya Sari, Mutia Nofita Sarmin, Nor Haniza Satriawan, Didit Semil @ Ismail, Ghazali Semil Ismail, Ghazali Shaumi, Nurina Fadlila Siboro, Ayes Malona Siti Raudhatul Kamali Sudiantoro, Beni Nungroho Sudirman Sudirman Surya Hadi Suwastika, Erma Syafitri, Hanna Syaftirridho Putri Syawaludin, Muhammad Khair Tri Dharmayani, Ni Komang Tri Maryono Rusadi Ubaidillah, Moch Rafi Zarkasy Wahidah, Fathul Maulina Widiastuti, Ratna Sari Yatin, Bela Zainun Zata Yumni Awanis Zata Yumni Awanis Zata Yumni Awaris