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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
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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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

Graf nilpoten dari gelanggang bilangan bulat modulo merupakan salah satu representasi graf pada struktur aljabar. Penelitian ini bertujuan mencari bentuk dan sifat graf nilpoten dari gelanggang bilangan prima modulo yang kemudian digeneralisasi menjadi gelanggang bilangan bulat modulo berpangkat prima sebarang. Metode yang digunakan pada penelitian ini adalah studi literatur. Pada gelanggang bilangan prima modulo, diperoleh bentuk graf nilpotennya adalah suatu graf bintang. Kemudian karakteristik dari graf nilpoten pada gelanggang bilangan bulat modulo berpangkat prima sebarang adalah memuat subgraf lengkap dan memuat buah subgraf bintang .
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.
The Szeged Index and Padmakar-Ivan Index on the Zero-Divisor Graph of a Commutative Ring Ambar, Jinan; I Gede Adhitya Wisnu Wardhana; Abdurahim
Contemporary Mathematics and Applications (ConMathA) Vol. 7 No. 1 (2025)
Publisher : Universitas Airlangga

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20473/conmatha.v7i1.63517

Abstract

The zero-divisor graph of a commutative ring is a graph where the vertices represent the zero-divisors of the ring, and two distinct vertices are connected if their product equals zero. This study focuses on determining general formulas for the Szeged index and the Padmakar-Ivan index of the zero-divisor graph for specific commutative rings. The results show that for the first case of ring, the Szeged index is exactly half of the Padmakar-Ivan index. For the second case, the Szeged index is consistently greater than the Padmakar-Ivan index. These findings enhance the understanding of how the algebraic structure of rings influences the topological properties of their associated graphs.
Meningkatkan Keterampilan dan Kreativitas Siswa Menggunakan Implementasi Teori Domino di SMAN 1 Batukliang Utara Ayes Malona Siboro; Fathul Maulina Wahidah; Lalu Riski Wirendra Putra; Sahin Two Lestari; Syaftirridho Putri; Rendi Bahtiar Pratama; I Gede Adhitya Wisnu Wardhana
Pemberdayaan Masyarakat : Jurnal Aksi Sosial Vol. 1 No. 3 (2024): September : Pemberdayaan Masyarakat: Jurnal Aksi Sosial
Publisher : Lembaga Pengembangan Kinerja Dosen

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62383/aksisosial.v1i3.638

Abstract

In this era of globalization, having critical and creative thinking skills is a capability that students must possess to compete and face the future. Community service conducted at SMAN 1 Batukliang Utara aimed at developing students’ skills and creativity was carried out by adopting the domino theory approach. The results of the pre-test showed that the average student score after statistical testing was 64.06. However, after participating in the community service activities and taking the post-test, the average score increased to 89.81, indicating an improvement in students’ understanding by 40.20%.
Pelatihan Pembuatan dan Penggunaan Pupuk Organik Cair dari Urine Sapi untuk Tanaman Hortikultura di Desa Sukadana, Kecamatan Pujut, Kabupaten Lombok Tengah Beni Nungroho Sudiantoro; Adelia Adelia; Devia Arisanti; Ilham Ilham; Arzaki Zaget Oasis; M. Afdhol Gilman; Munawara Putia; Aenan Salsabila; Ida Rohani; Anisa Agustina; I Gede Adhitya Wisnu Wardhana
Sinergi dan Harmoni Masyarakat MIPA Vol. 1 No. 2 (2025): April
Publisher : Fakultas Matematika dan Ilmu Pengetahuan Alam

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/sinonim.v1i2.70-77

Abstract

The Community Service Program for Village Empowerment (KKN-PMD) at the University of Mataram (UNRAM) was conducted on January 16, 2024, in Sukadana Village, Pujut District, Central Lombok Regency, to empower farmers in utilizing livestock waste as liquid organic fertilizer (POC) from cow urine. This initiative aims to enhance soil fertility, reduce dependence on chemical fertilizers, and promote sustainable agriculture. Additionally, the use of livestock waste for POC production is expected to minimize environmental pollution caused by unmanaged cow urine disposal. Using the Participatory Action Research (PAR) approach, the program engaged farmers in training and hands-on practice to produce POC using cow urine, EM4, and molasses. The results showed that POC improved soil fertility, restored soil structure, and increased agricultural yields by 15–20% while reducing production costs. Beyond economic benefits, this program encourages farmers to adopt environmentally friendly agricultural practices and introduces a more sustainable fertilizer alternative. The improved knowledge and skills in waste management are expected to have a lasting positive impact on sustainable farming in Sukadana Village and serve as a model for other regions with similar agricultural conditions.
Energy and Degree Sum Energy of Non-coprime Graphs on Dihedral Groups Karang, Gusti Yogananda; Wardhana, I Gede Adhitya Wisnu; Alimon, Nur Idayu; Sarmin, Nor Haniza
Journal of the Indonesian Mathematical Society Vol. 31 No. 1 (2025): MARCH
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.v31i1.1900

Abstract

Research on graphs has increasingly garnered attention in recent years.This research focuses on graph representations, with particular emphasis on non-coprime graphs within the dihedral group D_{2n} with n = p^k, prime numbers, $k \in \mathbb{Z}^+$. The non-coprime graph of a group G is defined as a graph in which the vertex set is G \{e}, and two distinct vertices r and s are connected by an edge if gcd(|r|,|s|) =\= 1. Specifically, this research examines the adjacency matrix energy and the degree sum energy of non-coprime graphs on dihedral groups. With the extensive application of chemical topological graphs in the field of chemistry, it is hoped that they can assist in the numerical analysis of chemical compounds used in healthcare, such as the analysis of vaccines for the COVID-19 epidemic.
Analisis Strategi Pemasaran KFC dan McDonald’s pada Masa Boikot Menggunakan Teori Permainan: Studi Kasus Mahasiswa Universitas Mataram Ubaidillah, Moch Rafi Zarkasy; Febrilia, Baiq Rika Ayu; Wardhana, I Gede Adhitya Wisnu
Griya Journal of Mathematics Education and Application Vol. 5 No. 2 (2025): Juni 2025
Publisher : Pendidikan Matematika FKIP Universitas Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/griya.v5i2.568

Abstract

The impact of boycotts against global brands has directly influenced the marketing approaches of fast-food companies such as KFC and McDonald’s. This study aims to identify the most effective marketing strategies that both companies can adopt in response to these challenges. The research utilizes a two-player game theory model with a mixed strategy approach, analyzed through matrix algebra—specifically involving calculations of cofactors, adjoints, and determinants. Data were collected via questionnaires distributed to 100 students at the University of Mataram, focusing on four key strategic variables: communication, promotion, innovation, and service. The response matrices were simplified using row and column dominance elimination before further analysis. The results show that KFC’s optimal strategy consists of a combination of 60% innovation and 40% promotion. In contrast, McDonald’s performs best with a balanced strategy, applying 50% promotion and 50% innovation. A game value of –12 indicates that McDonald’s holds a relative advantage in minimizing potential losses during the boycott period. This study contributes valuable insights into quantitative marketing strategy analysis using a mathematical framework.
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