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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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The Decomposition of a Finitely Generated Module over Some Special Ring Wardhana, I Gede Adhitya Wisnu
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 6, No 2 (2022): April
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v6i2.6769

Abstract

This research aims to give the decompositions of a finitely generated module over some special ring, such as the principal ideal domain and Dedekind domain. One of the main problems with module theory is to analyze the objects of the module. This research was using a literature study on finitely generated modules topics from scientific journals, especially those related to the module theory. And by selective cases we find a pattern to build a conjecture or a hypothesis, by deductive proof, we prove the conjecture and state it as a theorem. The main result in this study is the decomposition of the finitely generated module is a direct sum of the torsion submodule and torsion-free submodule.  Since the torsion-free module is always a free module over a principal ideal domain, then the torsion-free submodule is a free module. Last, we generalize the ring, from a principal ideal domain, to a Dedekind domain. We found then the torsion-free submodule became a projective module.  Then the decomposition of the finitely generated module is a direct sum of the torsion submodule and the projective submodule. These results should help the researchers to analyze the objects on module theory. 
Studi Teoretis Indeks Sombor pada Graf-Graf yang Dikonstruksi dari Grup Hingga Hapsari, Mufidatul Ghina; Wardhana, I Gede Adhitya Wisnu; Abdurahim, Abdurahim
Mandalika Mathematics and Educations Journal Vol 7 No 4 (2025): Desember
Publisher : FKIP Universitas Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/jm.v7i4.10674

Abstract

Penelitian ini membahas penerapan Indeks Sombor pada berbagai jenis graf yang dibangun dari struktur grup hingga. Indeks Sombor merupakan salah satu indeks topologi yang digunakan untuk mengukur karakteristik graf melalui derajat simpul yang saling berhubungan. Penelitian ini difokuskan pada penentuan pola umum dan perbandingan nilai Indeks Sombor pada beberapa jenis graf grup, yaitu graf koprima, graf non-koprima, graf unit, graf nilpoten, dan graf pangkat. Metode penelitian yang digunakan bersifat teoretis dengan pendekatan kajian pustaka dan analisis deduktif. Setiap graf dikonstruksi berdasarkan relasi antar elemen grup, kemudian derajat simpul ditentukan untuk menghitung nilai Indeks Sombor secara sistematis. Hasil penelitian menunjukkan adanya perbedaan karakteristik nilai Indeks Sombor yang bergantung pada sifat struktur grup yang digunakan, baik komutatif maupun non-komutatif. Selain itu, diperoleh pola umum yang dapat digunakan sebagai dasar untuk menganalisis keterkaitan antara struktur aljabar grup dan sifat topologis grafnya. Temuan ini diharapkan dapat memperkaya kajian energi graf dan indeks topologi dalam konteks teori graf aljabar.
GRAPH ENERGY OF THE COPRIME GRAPH ON GENERALIZED QUATERNION GROUP Miftahurrahman, Miftahurrahman; Wisnu Wardhana, I Gede Adhitya; Alimon, Nur Idayu; Sarmin, Nor Haniza
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss1pp0031-0040

Abstract

This paper investigates the Degree Square Sum Energy , Degree Exponent Energy , and Degree Exponent Sum Energy of the coprime graph on generalized quaternion group ​. This research is quantitative study using previous study as the literature review to construct the new theorem. These energy methods provide new insights into the spectral properties of graphs by their vertex degree distributions into eigenvalue computations. Using spectral graph theory, the general formulas for the , , and of ​ are formulated for for every positive integer . Furthermore, we explore the implications of these methods in understanding the algebraic and spectral characteristics of ​. Numerical results are presented for specific cases to validate the previous theorem. This study contributes to the broader analysis of graph energies, offering a framework for studying other algebraic structures.
A Novel Approach to Topological Indices of the Power Graph Associated with the Dihedral Group of a Certain Order Syarifudin, Abdul Gazir; Santi, Laila Maya; Shaumi, Nurina Fadlila; Suwastika, Erma; Wardhana, I Gede Adhitya Wisnu
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; Hidayat, Muhammad Ahsan; Dharmayani, Ni Komang Tri; Wardhana, I Gede Adhitya Wisnu
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.
Implementasi Pembelajaran Coding Dan Kriptografi Pada Pesan Digital di SMA Negeri 2 Mataram Maulani Rizqi; Intan Nadilah; Ahmadil Hamdi; Nikken Prima Puspita; I Gede Adhitya Wisnu Wardhana
Pemberdayaan Masyarakat : Jurnal Aksi Sosial Vol. 2 No. 4 (2025): Desember: Pemberdayaan Masyarakat : Jurnal Aksi Sosial
Publisher : Lembaga Pengembangan Kinerja Dosen

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.62383/aksisosial.v2i4.2641

Abstract

This community service activity aims to increase the understanding of students at State Senior High School 2 Mataram regarding information security by introducing the concepts of coding and cryptography in digital messages. The rapid use of messaging applications among teenagers makes students increasingly vulnerable to cyber threats, necessitating education on how data protection works in online communication. This program is implemented using a descriptive method consisting of planning, implementation, and evaluation stages. The material covered includes basic cryptography concepts, end-to-end encryption mechanisms, and the practical process of the Diffie–Hellman key exchange thru the interactive simulation "Alice and Bob." Learning is designed contextually and participatively so that students can connect theory with the digital applications they use every day. The evaluation results showed an improvement in students' understanding, reflected in their active participation, ability to answer questions, and adequate post-test scores. This activity not only strengthens digital security literacy but also raises students' awareness of the importance of protecting personal data in online communication. This program is expected to be the beginning of more sustainable digital security learning development in the school environment.
BOILING POINT MODELING OF EUGENOL COMPOUNDS AND ITS DERIVATIVES USING THE SOMBOR INDEX AND REDUCED SOMBOR INDEX APPROACHES Ardana, Alfian Putra; Putri, Syaftirridho; Lestari, Dia; Wardhana, I Gede Adhitya Wisnu; Dharmayani, Ni Komang Tri
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.
SOME CHEMICAL TOPOLOGICAL INDICES FOR THE COPRIME GRAPH OF THE INTEGERS MODULO GROUP Elfiyanti, Gustina; Sari, Mutia Nofita; Wisnu Wardhana, I Gede Adhitya; Candra, Ade; Semil Ismail, Ghazali
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 2 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss2pp0971-0980

Abstract

This paper delves into the exploration of the coprime graph of a finite group G, a graph with vertices representing all group elements. Vertices x and y are considered adjacent in ΓG if their orders are relatively prime. Specifically, our focus lies in determining essential topological indices: the first Zagreb index, the second Zagreb index, and the Wiener index of the coprime graph associated with the group of integers modulo n. The groups under consideration in this study are those of integers modulo n, where n takes the form of prime power and multiplication of two prime powers, with p and q representing distinct prime numbers and r and s representing natural numbers. This investigation aims to provide a comprehensive understanding of the structural and numerical properties of the coprime graph within the context of finite groups, shedding light on the intricate relationships between group elements and their algebraic properties.
COMPUTATIONAL ANALYSIS OF TOPOLOGICAL INDICES ON POWER GRAPHS OF MODULO PRIME POWER GROUPS USING PYTHON Qudrani , Rabbelia Tri; Rusadi, Tri Maryono; Wardhana, I Gede Adhitya Wisnu; Syarifudin, Abdul Gazir
MATHunesa: Jurnal Ilmiah Matematika Vol. 13 No. 3 (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.
Pengenalan Algoritma Dengan Menggunakan Aplikasi Scratch Jr Di SMAN 1 Pemenang Lombok Utara Abdullah, Umar; Syawaludin, Muhammad Khair; Hisan, Khairatun; Indrawadi, Dimas; Rohiana, Siti Indah; Ma'wa, Jannatul; Qudrani, Rabbelia; Musyarrofah, Sefti Fajriatul; Apriliana, Haeva; Wardhana, I Gede Adhitya Wisnu; Maulana, Fariz
Sinergi dan Harmoni Masyarakat MIPA Vol. 2 No. 1 (2025): Oktober
Publisher : Fakultas Matematika dan Ilmu Pengetahuan Alam

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/sinonim.v2i1.7808

Abstract

This community service program aimed to introduce fundamental algorithmic concepts to high school students using a visual, interactive approach through the Scratch Jr application. The activity took place at SMAN 1 Pemenang, North Lombok, as part of the MBKM program by mathematics students of Universitas Mataram. This initiative responded to the growing need for computational thinking and logical reasoning as key skills in 21st-century education. The program involved a series of stages: preparatory meetings, delivery of instructional materials, and hands-on practice. A pre-test and post-test were administered to measure students’ understanding before and after the activity. Statistical analysis using a paired sample t-test in SPSS revealed a significant improvement in students' scores (mean pre-test: 5.81; post-test: 9.06; p < 0.001), demonstrating the effectiveness of the Scratch Jr-based learning method. These findings emphasize the potential of visual programming tools to enhance students’ logical reasoning and computational literacy. The success of this activity also suggests the importance of integrating digital technology in classroom instruction and the value of teacher training in using such tools.
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