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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 Matematika UNAND 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 MATHunesa: Jurnal Ilmiah Matematika Journal of Fundamental Mathematics and Applications (JFMA) NUSANTARA: Jurnal Pengabdian Kepada Masyarakat Jurnal Pepadu Basis : Jurnal Ilmiah Matematika Jurnal Pengabdian Inovasi Masyarakat Indonesia Pemberdayaan Masyarakat: Jurnal Aksi Sosial Sinergi dan Harmoni Masyarakat MIPA E-Jurnal Matematika
I Gede Adhitya Wisnu Wardhana
Department Of Mathematics, Faculty Of Mathematics And Natural Science, University Of Mataram
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A Novel Approach to Topological Indices of the Power Graph Associated with the Dihedral Group of a Certain Order Abdul Gazir Syarifudin; Laila Maya Santi; Nurina Fadlila Shaumi; Erma Suwastika; I Gede Adhitya Wisnu Wardhana
Eigen Mathematics Journal Vol 8 No 2 (2025): December
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v8i2.253

Abstract

Power graph of a group G, represented by \Gamma_G, is a graph where the vertex set consists of the elements of G. Two distinct vertices a, b \in G are connected by an edge if and only if there exists a positive integer m such that a^m = b or b^m = a. This study explores the utilization of a new approach to compute the topological indices of power graph associated with dihedral group with n=p^k, p is primes and k \in \mathbb{Z}. Results obtained indicate that the topological indices calculated using new approach yield the same values as those obtained with the conventional approach.
Analysis of the Relationship Between Second Zagreb Index Values and the Oxidation Levels of Terpenoid Derivatives Luzianawati Luzianawati; Muhammad Ahsan Hidayat; Ni Komang Tri Dharmayani; I Gede Adhitya Wisnu Wardhana
Eigen Mathematics Journal Vol 8 No 2 (2025): December
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v8i2.264

Abstract

Terpenoids are a group of secondary metabolites composed of isoprene units containing five carbon atoms (C5), synthesized from acetate through the mevalonate pathway. This research examines two triterpenoid derivatives, densiflorinic acid A and densiflorinic acid B. The second Zagreb index is applied to illustrate atomic interaction patterns—including H--C, C--O, O--H, and C--C—which serve as indicators of molecular structural complexity. The findings indicate that the second Zagreb index is a reliable measure for assessing the structural complexity and oxidation levels of triterpenoid derivatives that share the same core framework.
Analysis of Topological Indices in Unit Graphs of Modular Integer Rings Ashadul Umam; Abdul Gazir Syarifudin; Erma Suwastika; I Gede Adhitya Wisnu Wardhana
Eigen Mathematics Journal Vol 9 No 1 (2026): June
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v9i1.306

Abstract

Topological indices are numerical graph invariants that reflect structural properties of graphs and have broad applications in chemistry, algebra, and network analysis. This paper focuses on the analysis of several topological indices in the context of unit graphs associated with modular integer rings. In a unit graph, vertices represent ring elements, and two vertices are adjacent if their sum is a unit. We investigate and derive general formulas for six indices: the Narumi-Katayama index, the Forgotten index, the Atom-Bond Connectivity (ABC) index, the first and second Gourava indices, and the first Revan index. Two cases are considered for the ring of integers modulo $n$, namely when $n$ is a power of $2$ and when $n$ is an odd prime. The results offer a deeper understanding of the algebraic and combinatorial properties of unit graphs and contribute to the development of algebraic graph theory.
COMPUTATIONAL ANALYSIS OF TOPOLOGICAL INDICES ON POWER GRAPHS OF MODULO PRIME POWER GROUPS USING PYTHON Rabbelia Tri Qudrani; Tri Maryono Rusadi; I Gede Adhitya Wisnu Wardhana; Abdul Gazir Syarifudin
MATHunesa: Jurnal Ilmiah Matematika Vol. 13 No. 03 (2025)
Publisher : Universitas Negeri Surabaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26740/mathunesa.v13n3.p459-465

Abstract

This study uses Python to calculate and analyze three indices such as the first Zagreb, Wiener, and Gutman indices on the rank graph of the group modulo the power of a prime number. It relies on formulas that have been developed by previous research. By using Python libraries such as NetworkX, Matplotlib, and Tkinter, the calculation process becomes more efficient and allows visualization of index variations based on changes in the values of prime p and exponent k. The results show that the values of the three indices increase as the values of p and k increase, reflecting the increasing complexity of the graph structure. At large values of p and k, the graph visualization is too complex which causes the graph visualization to be less clear. This approach proves to be effective in supporting visual and quantitative exploration of algebraic structures.
IMPLEMENTATION ON DIFFERENTIAL EQUATION OF MILNE-SIMPSON FOR PREDICTION FOR APPARENT POWER USAGE IN PLN (PERSERO) UIW NTB FITRAH RAMADHAN; RIO SATRIYANTARA; YUNITA SEPTRIANA ANWAR; I GEDE ADHITYA WISNU WARDHANA
E-Jurnal Matematika Vol. 15 No. 3 (2026)
Publisher : Mathematics Department, Faculty of Mathematics and Natural Sciences, Udayana University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24843/MTK.2026.v15.i03.p509

Abstract

Electricity is one of the essential forms of energy required by humans in modern society. Consequently, the demand for electricity supply will continue to increase over time. Irregular or fluctuating electricity consumption can affect the readiness of power generation units to provide an adequate supply of electricity to consumers or the public. By predicting apparent power (VA), power companies can optimize generation efficiency, ensure grid stability, and reduce losses. This study applies the logistic equation model using annual apparent power usage data obtained from PT PLN (Persero) UIW NTB for the 2011–2024 period. The model parameters (growth rate r and carrying capacity K) were estimated directly from the historical data, and the differential equation was solved numerically using the Milne-Simpson method with initial values generated by the fourth-order Runge-Kutta approach. The logistic model is chosen for its ability to represent nonlinear growth toward a saturation capacity. Simulation results show a gradually increasing trend in VA usage that slows down as it approaches the saturation phase around 2030. Model validation, performed by comparing the numerical predictions with the actual historical data, shows very small relative errors ranging from 10⁻⁵ to 10⁻⁷, confirming that the Milne-Simpson method possesses high accuracy and stability.
BOILING POINT MODELING OF EUGENOL COMPOUNDS AND ITS DERIVATIVES USING THE SOMBOR INDEX AND REDUCED SOMBOR INDEX APPROACHES Alfian Putra Ardana; Syaftirridho Putri; Dia Lestari; I Gede Adhitya Wisnu Wardhana; Ni Komang Tri Dharmayani
Journal of Fundamental Mathematics and Applications (JFMA) Vol 8, No 2 (2025)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v8i2.25725

Abstract

Eugenol and its derivatives, phenylpropanoid compounds derived from plants like Syzygium aromaticum, exhibit significant biological activities, including antimicrobial, antifungal, anti-inflammatory, antioxidant, analgesic, and anticancer properties. These attributes make them valuable in drug development and medical applications. In mathematical chemistry, chemical topology graphs are used to determine the topological indices of molecules, which to help predict physical and chemical properties. Here, atoms are represented as nodes and bonds as edges. This study explores the relationship between the Sombor index, the reduced Sombor index, and the boiling points of eugenol and its derivatives. The methodology includes literature review and computational analysis of the indices, followed by correlation analysis with the boiling points. The findings reveal that the Sombor index negatively correlates with the boiling point, explains 84.8% of the boiling point variance. This implies that an increase in the Sombor index results in a lower boiling point. Conversely, the reduced Sombor index demonstrates a positive correlation, influencing 36.1% of the boiling point variations, indicating that higher reduced Sombor indices correspond to higher boiling points. When combined, the Sombor and reduced Sombor indices explain 86.4% of the boiling point variance, highlighting their significance as predictive parameters. These results provide insights into the thermal properties of eugenol-based compounds and their potential applications in material and pharmaceutical sciences. By leveraging these indices, researchers can better predict and tailor the physical properties of eugenol derivatives for specific purposes.
INDEKS WIENER PADA GRAF KOPRIMA PRIMA DARI GRUP BILANGAN BULAT MODULO Abdurahim Abdurahim; LIA FITTA PRATIWI; GUSTI YOGANANDA KARANG; I GEDE ADHITYA WISNU WARDHANA; MAMIKA UJIANITA ROMDHINI
Jurnal Matematika UNAND Vol. 15 No. 2 (2026)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.15.2.249-258.2026

Abstract

Graf Koprima Prima merupakan graf yang mana sebarang dua simpul berbeda dikatakan bertetangga jika dan hanya jika Faktor Persekutuan terbesar (FPB) dari order kedua simpul sama dengan 1 atau prima. Penelitian ini bertujuan untuk mengkaji subgraf serta rumus umum dari indeks Wiener dan Hyper-Wiener pada graf koprima prima dari grup bilangan bulat. Dari penelitian ini didapatkan bahwa subgraf yang terbentuk adalah graf lengkap dan bipartit. Selain itu, diperoleh juga rumus umum indeks Wiener dan Hyper-Wiener. Lebih jauh, nilai dari indeks Hyper-Wiener kurang dari dua kali indeks Wiener.
Predicting Customer Numbers at PT PLN (Persero) West Nusa Tenggara Regional Main Unit Using the Prophet Time Series Model Rida Alkausar Hardi; Rio Satriyantara; Yunita Septriana Anwar; I Gede Adhitya Wisnu Wardhana
Contemporary Mathematics and Applications (ConMathA) Vol. 8 No. 2 (2026)
Publisher : Universitas Airlangga

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20473/conmatha.v8i2.88166

Abstract

Electricity is a fundamental need for modern society, and in developing regions such as West Nusa Tenggara, the continuous growth in the number of customers requires PT PLN (Persero) to conduct effective resource planning to prevent potential energy crises. This study aims to predict the growth of PLN’s customer numbers using the Facebook Prophet time series model. A quantitative approach was applied using monthly customer data from PT PLN (Persero) covering the period from January 2019 to December 2024. The model was optimized through a hyperparameter tuning process, and its performance was evaluated using the Mean Absolute Percentage Error (MAPE) metric. The results demonstrate that the optimized model achieved a MAPE of 0.27% during cross-validation. Analysis of the results indicates that the model effectively captured long-term growth trends and seasonal fluctuations. These findings suggest that the Prophet model can serve as a technical reference for forecasting customer numbers, potentially supporting strategic decision-making and resource allocation at PT PLN (Persero).
Hyper-Wiener and Harary Indices of The Line Graph of Zero Divisor Graph For Integer Modulo Ring Fariz Maulana; I Gede Adhitya Wisnu Wardhana
Jurnal Matematika, Statistika dan Komputasi Vol. 22 No. 3 (2026): May 2026
Publisher : Department of Mathematics, Hasanuddin University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20956/j.v22i3.48758

Abstract

This paper studies the line graph of the zero divisor graph of the ring Z_(P^n ), where p is a prime and n is a natural number. The main objective is to compute closed formulas for the Hyper–Wiener and Harary indices of the line graph L(〖ΓZ〗_(P^n ) ) and to analyze their relationship with the first Zagreb index of the original graph ΓZ_(P^n ). The results establish connections between structural properties of the zero divisor graph and those of its corresponding line graph, offering a deeper understanding of interactions among degree-based and distance-based topological indices.
The Non-Normal Cyclic Subgroup Graph Associated with Quasidihedral Groups of Order 16 Nur Nabilah Abdul Razak; Nur Idayu Alimon; Adem Kilicman; Nor Haniza Sarmin; Nabilah Fikriah Rahin; I Gede Adhitya Wisnu Wardhana
Journal of the Indonesian Mathematical Society Vol. 32 No. 3 (2026): SEPTEMBER
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.v32i3.2140

Abstract

Let \textsl{G} be a group and \textsl{H} be a non-normal cyclic subgroup of \textsl{G}. The non-normal cyclic subgroup graph, denoted as $\Gamma^{NN}_{H}(G)$, is defined as a directed graph with vertex set elements of \textsl{G} such that for two distinct elements \textsl{x} and \textsl{y} in \textsl{G}, \textsl{x} is the initial vertex and \textsl{y} is the terminal vertex of an edge if their product is in \textsl{H}. In 2020, the idea of the non-normal subgroup graph, which is the extension of the subgroup graph was developed. This research identifies the non-normal cyclic subgroup graphs connected to order 16 quasidihedral groups. Firstly, the Groups, Algorithms and Programming (GAP) software is used to identify the non-normal cyclic subgroups. The definition of $\Gamma^{NN}_{H}(G)$ is then used to calculate the adjacency and direction of the vertices. Lastly, Maple 2016 software will be used to visualize these graphs.
Co-Authors @ Ismail, Ghazali Semil A.A. Ketut Agung Cahyawan W Abdul Gazir Syarifudin Abdul Gazir Syarifudin Abdurahim, Abdurahim Adelia Adelia Adelia Adelia, Adelia Adem Kilicman Aenan Salsabila Afdhaluzzikri, M. Ahmadil Hamdi Albaracin, Jimboy R. Alfian Putra Ardana Alfian Putra Ardana Alimon, Nur Idayu Ambar, Jinan Angamuthu, Manimaran Anisa Agustina Anisa Agustina, Anisa Arisanti, Devia Arzaki Zaget Oasis Ashadul Umam 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 De Siroj Ragil Ahmad Deny Putra Malik Devia Arisanti Dia Lestari Dina Eka Putri Dwi Noorma Putri Emmy Yuanita Erma Suwastika Evi Yunartika Asmarani Evi Yuniartika Asmarani Evi Yuniartika Asmarani Evi Yuniartika Asmarani Fadhilah, Rifdah Fariz Maulana Fariz Maulana Farwan, Farwan Fathul Maulina Wahidah Febrilia, Baiq Rika Ayu FITRAH RAMADHAN Gayatri, Marena Rahayu Ghazali Semil @ Ismail Ghazali Semil Ismail Ghoffari, Lalu Hasan Gifani Putri Setiandini Gilman, M. Afdhol Graha, Syifa Salsabila Satya Gusti Yogananda Karang Haryati, Ida Hijriati, Naimah Husni, Muhammad Naoval I Nengah Suparta Ida Rohani Ilham Ilham Ilham Ilham Intan Muchtadi Alamsyah Intan Nadilah Irene Rainbow Kewa Somi Irene Salsabila Irwansyah Irwansyah Irwansyah Irwansyah Irwansyah Irwansyah Jurnal Pepadu Karang, Gusti Yogananda Laila Hayati Laila Maya Santi Lailia Awalushaumi Lalu Hasan Ghoffari Lalu Hasan Ghoffari Lalu Muhammad Faiz Zikri Lalu Riski Wirendra Putra Lalu Riski Wirendra Putra Lestari, Sahin Two Lia Fitta Pratiwi Lia Fitta Pratiwi Luluk Kartika Luzianawati Luzianawati M Fauzul M. Afdhol Gilman Malik, Deny Putra Mamika Ujianita Romdhini MAMIKA UJIANITA ROMDHINI Maria Ulfa Marwan Marwan Masriani Masriani Masriani Masriani Maulana, Fariz Maulana, Muklas Maulani Rizqi Maulida Septiyana MAXRIZAL Miftahurrahman, Miftahurrahman Misuki, Wahyu Ulyafandhie Mufarrihati, Ardelia Muhammad Ahsan Hidayat Muhammad Naoval Husni Muhammad Rijal Alfian Muklas Maulana Munawara Putia Nabilah Fikriah Rahin Nanda Lestari Nghiem, Nguyen Dang Hoa Ni Komang Tri Dharmayani Ni Komang Tri Dharmayani Ni Wayan Switrayni Ni Wayan Switrayni Ni Wayan Switrayni Nikken Prima Puspita Ningsih, Baiq Nila Sari Nor Haniza Sarmin Nur Asmita Purnamasari Nur Idayu Alimon Nur Idayu Alimon Nur Nabilah Abdul Razak Nurhabibah Nurhabibah Nurhabibah Nurhabibah Nurhabibah Nurhabibah Nurina Fadlila Shaumi 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 Putu Kartika Dewi Qurratul Aini Qurratul Aini Qurratul Aini Rabbelia Tri Qudrani Ramdani, Dewi Santri Rendi Bahtiar Pratama Resa Putri Fibriyanti Subiyanto Rida Alkausar Hardi Rina Juliana Rina Juliana Rio Satriyantara Rizka Purnama Sari Robbaniyyah, Nuzla Af’idatur Rohani, Ida Sabil, M. Ibnu Sahin Two Lestari Sahin Two Lestari Sahin Two Lestari Salsabila, Aenan Salwa Salwa Salwa Salwa Salwa Salwa Salwa Salwa Salwa Salwa Sarmin, Nor Haniza Satriawan, Didit Semil @ Ismail, Ghazali Siboro, Ayes Malona Siti Raudhatul Kamali Sudiantoro, Beni Nungroho Sudirman Sudirman Surya Hadi Syafitri, Hanna Syaftirridho Putri Syaftirridho Putri Syamsul Bahri Tri Dharmayani, Ni Komang Tri Maryono Rusadi Ubaidillah, Moch Rafi Zarkasy Wahidah, Fathul Maulina Widiastuti, Ratna Sari Yatin, Bela Zainun Yunita Septriana Anwar Zata Yumni Awanis Zata Yumni Awanis Zata Yumni Awaris