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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 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