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Journal : Contemporary Mathematics and Applications (ConMathA)

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.
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.
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