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Journal : EIGEN MATHEMATICS JOURNAL

Algebraic Structures and Combinatorial Properties of Unit Graphs in Rings of Integer Modulo with Specific Orders Lestari, Sahin Two; Dewi, Putu Kartika; Wardhana, I Gede Adhitya Wisnu; Suparta, I Nengah
Eigen Mathematics Journal Vol 7 No 2 (2024): December
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v7i2.235

Abstract

Unit graph is the intersection of graph theory and algebraic structure, which can be seen from the unit graph representing the ring modulo n in graph form. Let R be a ring with nonzero identity. The unit graph of R, denoted by G(R), has its set of vertices equal to the set of all elements of R; distinct vertices x and y are adjacent if and only if x + y is a unit of R. In this study, the unit graph, which is in the ring of integers modulo n, denoted by G(Zn). It turns out when n is 2^k, G(Zn) forms a complete bipartite graph for k∈N, whereas when n is prime, G(Zn) forms a complete (n+1)/2-partites graph. Additionally, the numerical invariants of the graph G(Zn), such as degree, chromatic number, clique number, radius, diameter, domination number, and independence number complement the characteristics of G(Zn) for further research.
Hyper-Wiener and Szeged Indices of non-Coprime Graphs of Modulo Integer Groups Ghoffari, Lalu Hasan; Wardhana, I Gede Adhitya Wisnu; Dewi, Putu Kartika; Suparta, I Nengah
Eigen Mathematics Journal Vol 8 No 1 (2025): June
Publisher : University of Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29303/emj.v8i1.244

Abstract

The non-coprime graph of the integer modulo group is a graph whose vertices represent the elements of the integer modulo group, excluding the identity element. Two distinct vertices are adjacent if and only if their orders are not relatively prime. This study explores two topological indices, the Hyper-Wiener index and the Szeged index, in the non-coprime graph of the integer modulo-n group. The results reveal that these indices are equal when the order is a prime power but differ when the order is the product of two distinct prime numbers. This research provides new insights into the patterns and characteristics of these indices, contributing to a broader understanding of the application of graph theory to abstract group structures.
Co-Authors ., DR. I WAYAN SADRA, M.Ed. ., Gede Purwandika ., I Komang Widanto ., I Made Yoga Emma Prasetya ., I Pt Ade Andre ., I PUTU ADE ANDRE PAYADNYA ., I PUTU EDITIA MIUSENA ., I Wayan Kumarayasa ., IDA AYU IKA TRISNA DEWI ., IDA AYU NGURAH SULASMINIYATI ., KADEK YUDISTA WITRAGUNA ., MADE WIDYA SURYAPRANI ., NI KOMANG WIRASTI ., NI LUH TIA RAHMAWATI ., Ni Made Erlinta Devi ., Ni Made Irma Dwi Purnamayanti ., NI PUTU MEINA AYUNINGSIH ., NI WAYAN SANJIWANI UTAMI ., NI WAYAN SRI WIDHYANTARI ., NI WAYAN YUNIK WIDIA ASTUTI ., PANDE GEDE SUBIKSA BRAHMA RANDRA ., PUTU YULI SUWASTINI A. M. Sari Ade Dwi Utami Adi Saputra, Putu Resya Agustiari, Pande Kadek Rai Agustini, Kadek Trisna Anak Agung Lilyk Cahyani . Anak Agung Lilyk Cahyani ., Anak Agung Lilyk Cahyani Anak Agung Ngurah Gde Sapteka Annadhifi, Muhammad Ilham Nurfaizi Apriyanti, Muda Aritisna, Ni Made Tarisa Dian Bgeholz, Susanne Budayana, I Made Cahyani, Ni Putu Candra D. Dafik Dewa Ayu Oka Setiawati Dewi, Putu Kartika Dr. I Made Sugiarta, M.Si. . Dr.I Wayan Sadra,M.Ed . Drs.Djoko Waluyo,M.Sc . Eliska Juliangkary Findayani, Ni Kadek Gde Suweken Gede Purwandika . Gede Suweken Ghoffari, Lalu Hasan Gusti Ayu Mahayukti I Dewa M. Agus Ariawan I Dewa Made Agus Ariawan I Gede Adhitya Wisnu Wardhana I Gst Nyoman Yudi Hartawan I Gst Putu Sudiarta I GUSTI AGUNG EKA SURYANTARI . I Gusti Ngurah Pujawan I Gusti Nyoman Yudi Hartawan I GUSTI PUTU ARI SUGIANTARA . I Gusti Putu Suharta I Gusti Putu Suharta I KETUT GEDE BIRAWA ANURAGA . I Komang Sukendra I Komang Widanto . I Made Ardana I Made Chandra Adi Purnama I Made Satria Wiguna I Made Suarsana I Made Suarsana I Made Sumerta Yasa I Made Yoga Emma Prasetya . I MADE YOGA WICAKSANA . I Nyoman Gita I Nyoman Sukajaya I Pt Ade Andre . I Putu Ade Andre Payadnya I PUTU EKA IRAWAN I Putu Eka Irawan I Putu Wisna Ariawan I WAYAN EKA ARYASUTA . I Wayan Kumarayasa . I Wayan Muderawan I Wayan Puja Astawa I Wayan Sadra Ida Ayu Purnama Bestari Iswara, Dw. Md. Ananda Dian Juliangkary, Eliska K. DEADY IRMAWAN . Kadek Amerta Yasa Kadek Pasek Budarsini KANISIUS MANDUR . Komang Agus Widyatmika Komang Tri Purnamayanthi Lestari, Sahin Two LUH DE IRIN PRADNYAWATI . Luh Mitha Priyanka Luh Putu Sri Lestari Made Widya Suryaprani Matthiesen, Finn Muhammad Naoval Husni Muhammad Turmuzi N. K. Nuraini N. L. T Rahmawati Narita, Ni Luh Putu Dinna Surya Narottama, Anak Agung Ngurah Made Ni Kadek Findayani Ni Kadek Suryantini Ni Komang Wirasti Ni Luh Dewi Sintiari Ni Luh Putu Dinna Surya Narita Ni Luh Suciari . Ni Luh Suciari ., Ni Luh Suciari Ni Made Erlinta Devi . Ni Made Irma Dwi Purnamayanti . Ni Made Sri Mertasari Ni Made Suastini Ni Made Suastini, Ni Made Ni Made Suwarnisi Ni Nyoman Parwati Ni Nyoman Riantini W. Ni Putu Ari Wiratini Ni Putu Darmayanti Ni Putu Nova Andriani Ni Putu Santhi Widiasih NI PUTU WIWIN SURYANTARI . Ni Wayan Ekayanti Ni Wayan Mei Ekayanti Ni Wayan Sanjiwani Utami . Ni Wayan Sri Maeti Pande Kadek Rai Agustiari Partayasa, Wayan Payadnya, I Putu Ade Andre Periandani, Putu Novi Pratiwi, Kadek Ayu Mutiara Priyanka*, Luh Mitha Purnama, I Made Chandra Adi Purnamayanthi, Komang Tri Putra, Dewa Made Krisna Dharma Putra, Komang Hendri Nugraha Putu Adhitya Santika Dharma Putu Kartika Dewi Putu Nanci Riastini, Putu Nanci Putu Novi Periandani Putu Resya Adi Saputra Rahmawati, N. L. T Rani Darmayanti Riantini W., Ni Nyoman Riza Aldira Robiatul Adawiyah Sapteka, Anak Agung Ngurah Gde Sapteka Sariyasa . SEBASTIANUS FEDI . Setiawan, Kadek Aldi Setiawati, Dewa Ayu Oka Srinivasa, Putu Winy Suarningsih, Ni Luh Putu Ayu Intan Sudiarta, I Gst. Putu Suryantini, Ni Kadek Suryaprani, Made Widya Suweken, Gde Ulya, Viki Himatul Waluyo, D. Wayan Partayasa Wayan Sadra Wicaksana, I Made Yoga Widiantari, Ni Kadek Kasi Widiasih, Ni Putu Santhi Wikasari, Ayu Wirasti, Ni Komang