Claim Missing Document
Check
Articles

INDEKS WIENER PADA GRAF KOPRIMA PRIMA DARI GRUP BILANGAN BULAT MODULO Abdurahim, Abdurahim; PRATIWI, LIA FITTA; KARANG, GUSTI YOGANANDA; WARDHANA, I GEDE ADHITYA WISNU; ROMDHINI, MAMIKA UJIANITA
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.
Analysis of Topological Indices in Unit Graphs of Modular Integer Rings Umam, Ashadul; Syarifudin, Abdul Gazir; Suwastika, Erma; Wardhana, I Gede Adhitya Wisnu
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.
Estrada Index and Laplacian Estrada Index on the Non-Coprime Graph of the Dihedral Group of Prime PowerOrder Lia Fitta Pratiwi; I Gede Adhitya Wisnu Wardhana; Nur Idayu Alimon
Journal of Fundamental Mathematics and Applications (JFMA) Vol 9, No 1 (2026)
Publisher : Diponegoro University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/jfma.v9i1.26765

Abstract

Graphical representations of algebraic structures have become an important tool in modern mathematics and its applications. Graph theory, particularly spectral graph theory, is widely used across disciplines such as chemistry, physics, computer science, and network analysis to study structural and functional relationships. This study focuses on the non-coprime graph of the dihedral group \( D_{2n} \) with \(n=p^k \), where $p$ is a prime number, and \(k \in \mathbb{Z}^{+}\), analyzing two fundamental spectral parameters: the Estrada index and the Laplacian Estrada index, which are defined based on the eigenvalues of the graph’s adjacency and Laplacian matrices. The main result of this research is the derivation of explicit general formulas for both indices on the non-coprime graph of the dihedral group, contributing to the advancement of algebraic graph theory through spectral analysis.
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 Deny Putra Malik 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 Gusti Yogananda Karang 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 Lia Fitta Pratiwi 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 Nur Idayu Alimon 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 Umam, Ashadul Wahidah, Fathul Maulina Widiastuti, Ratna Sari Yatin, Bela Zainun Zata Yumni Awanis Zata Yumni Awanis Zata Yumni Awaris