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All Journal CAUCHY: Jurnal Matematika Murni dan Aplikasi BAREKENG: Jurnal Ilmu Matematika dan Terapan EIGEN MATHEMATICS JOURNAL Jurnal Diferensial Jurnal Pengabdian Inovasi Masyarakat Indonesia
Lestari, Sahin Two
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Journal : EIGEN MATHEMATICS JOURNAL

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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.
Co-Authors Abdurahim, Abdurahim Albaracin, Jimboy R. Asmarani, Evi Yuniartika Dewi, Putu Kartika Fadhilah, Rifdah Gayatri, Marena Rahayu Haryati, Ida I Gede Adhitya Wisnu Wardhana Pratama, Rendi Bahtiar Pratiwi, Lia Fitta Prof. Dr.I Nengah Suparta,M.Si . Purnamasari, Dara Putra, Lalu Riski Wirendra Putri, Syaftirridho Salwa Salwa Siboro, Ayes Malona Wahidah, Fathul Maulina