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Qurratul Aini
Program Studi Matematika FMIPA Universitas Mataram
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Journal : Contemporary Mathematics and Applications (ConMathA)

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Nilpotent Graphs of Rings of Integer Modulo: Structural Properties and Topological Indices Deny Putra Malik; Gusti Yogananda Karang; Qurratul Aini; I Gede Adhitya Wisnu Wardhana
Contemporary Mathematics and Applications (ConMathA) Vol. 8 No. 1 (2026)
Publisher : Universitas Airlangga

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20473/conmatha.v8i1.71177

Abstract

Nilpotent elements in modular rings play a fundamental role in understanding the algebraic structure of rings and their applications in various mathematical domains. Motivated by the need to explore the interplay between algebraic and combinatorial representations, this study introduces and investigates nilpotent graphs constructed from rings of integers modulo prime powers. We begin by characterizing nilpotent sets and establishing theorems that describe their distribution and algebraic behavior. Using these characterizations, we construct nilpotent graphs, where vertices represent nilpotent elements and edges reflect their interactions. The structural properties of these graphs are examined, and several well known topological indices, such as the Zagreb, Harary, Hyper Wiener, Randić, Harmonic, Sombor, and Schultz indices, are computed to quantify connectivity, complexity, and centrality. The results reveal meaningful patterns that bridge ring theory and graph theory.
Co-Authors . MUARDI A. Hamdani Abdul Gazir Syarifudin Abdul Hadi ABDURRAHMAN WAHID Adinda Nindia Candra Putri Amirullah Amelia Afitri Ananda Yulia Mayasari Azis Asnaini Asnaini Ayes Malona Siboro Azfa Aenurrohman Baiq Devi Rachmawati cahya Deny Putra Malik Dhany Safandi Dian Herdiana Dina Eka Putri Dwi Noorma Putri Era Pazira Evi Yuniartika Asmarani Faiz Muazirul Haq Febria Ningsih Fitriatul Hanisa Futri Ramadhani Gusman Lesmana Gusti Yogananda Karang Hafidhul Umami Hazanul Fuady Henny Marlina Heri Safriadi Hijrah I Gede Adhitya Wisnu Wardhana I Wayan Sudiarta INDRA YOVI Ira Damayanti Irval Huzairi Irwansyah Irwansyah Junaidi Junaidi Jurnal Pepadu Khanifatul Mardliyah Lailia Awalushaumi lailia Awalushaumi Lalu Hasan Ghoffari Lalu Riski Wirendra Putra Luluk Fauziyah Januarti M.Hasbi Marliadi Susanto Maryam, Ridha Dewi Masriani Masriani Maulana, Fariz Mawardi Moh Ma'ruf Moh. Syafi’i Idrus Muhamad Yahya Muhammad Azka Lababan Muhammad Farhan Muhammad Ibnu Andika Muhammad Maimunun Mubarok Muhammad Naoval Husni Muhammad Rijal Alfian Muhammad Yulis Hamidy Mustawa Mustika Hadijati MUTMAINNAH , Mutmainnah Mutmainnah Naila Dwi Salsabila Nazwa Zahara Ni Luh Putu Dewi Wikayanti Ni Wayan Switrayni Nisrina Fathin Nur Asmita Purnamasari Nur Diana Nurasiah Amini Nurhabibah Nurhabibah Nurul Fitriyani Nurul Mauidhotul Hasanah Nuzla Af'idatur Robbaniyyah Pahrudin Parizal Hidayatullah Qorri Asyifah Quratul A’yun Qurrotul Ainiyah Ridaaul Ummah Ridwal Trisoni Riskan Fauzy Rizal Afandi Rizki Maulana Rohayanti, Nurul Arma Rusindiyanto Ryan Dwipa S. Fathiyatul Jannah Sahrul Mubarok Salwa Salwa Salwa Salwa Salwa Salwa Salwa Salwa Sri Lestari Subaiah Marlina Syamsul Bahri Syofiarti Tsamratul Jannah Uci Faradilla Zaehol Fatah Zahratul Isnaini Zata Yumni Awanis Zata Yumni Awanis Zata Yumni Awaris Zulhan Widya Baskara