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Rio Satriyantara
Universitas Mataram
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Journal : Contemporary Mathematics and Applications (ConMathA)

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Numerical Invariants Of Nilpotent Graphs In Integer Modulo Rings Malik, Deny Putra; Karang, Gusti Yogananda; Aini, Qurratul; Maulana, Fariz; Satriyantara, Rio
Contemporary Mathematics and Applications (ConMathA) Vol. 7 No. 2 (2025)
Publisher : Universitas Airlangga

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20473/conmatha.v7i2.69650

Abstract

Graph theory offers a robust framework for examining algebraic structures, especially rings and their elements. This paper focuses on the nilpotent graph of rings of the form Zpk​, where p is a prime and k∈N, investigating both their structural and numerical properties. We begin by characterizing the nilpotent elements in these rings and examining their relationship to ring ideals. The study then presents theoretical results on key graph invariants, including connectivity, chromatic number, clique number, and specific subgraph configurations. To complement these, we also analyze numerical invariants such as edge count and degree distribution, which reveal deeper connections between ring-theoretic and graph-theoretic properties. Our results highlight consistent structural patterns in nilpotent graphs of Zpk ​and provide a concrete contribution to algebraic graph theory by bridging properties of commutative rings and their associated graphs.
Co-Authors Abdurahim, Abdurahim Ade Irawan Adi Irawan Alfian Eka Utama Alfian Eka Utama Alfian Eka Utama Ardana, Alfian Putra Ayes Malona Siboro Dara Puspita Anggraeni Dara Puspita Anggraeni Dara Puspita Anggraeni, Dara Puspita Dewi, Irma Risvana Dwi Agustini Dwi Agustini Dwi Agustini, Dwi Fariz Maulana Farwan Farwan Fathul Maulina Wahidah Fauzi, Andri Azmul Fauzi, Muhammad Hilmi Gusti Yogananda Karang Helmi Hariyanti Hidayat, Noor I Gede Adhitya Wisnu Wardhana Inayati, Rizqa Irma Risvana Dewi Irma Risvana Dewi Irma Risvana Dewi Irwansyah Irwansyah Karang, Gusti Yogananda Lalu Riski Wirendra Putra Lia Fitta Pratiwi Lilik Hidayati, Lilik Lismawanti Safitri Malik, Deny Putra Mamika Ujianita Romdhini Marhani Maulana, Fariz Pahrurrozi Pahrurrozi Qurratul Aini Rendi Bahtiar Pratama Ria Maulina Ridwan, Lalu Muhammad Ripai, Ripai Rismayatun Ainun Rohmah, Zulfiani Satriawan Pradana Suryanto, Agus Syaftirridho Putri Syifa Salsabila Satya Graha Tumilaar, Rinancy Utama, Alfian Eka Widiastuti, Ratna Sari Zarkasi Zarkasi Zata Yumni Awanis