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All Journal Journal of the Indonesian Mathematical Society BAREKENG: Jurnal Ilmu Matematika dan Terapan
Qonita, Niswah
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Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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BIPARTITE GRAPH ASSOCIATED WITH ELEMENTS AND COSETS OF SUBRINGS OF FINITE RINGS Muhammad, Hubbi; Qonita, Niswah; Wahyu Fibriyanti, R A; Susanti, Yeni
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 17 No 2 (2023): BAREKENG: Journal of Mathematics and Its Applications
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol17iss2pp0667-0672

Abstract

Let be a finite ring. The bipartite graph associated to elements and cosets of subrings of is a simple undirected graph with vertex set , where is the set of all subrings of , and two vertices and are adjacent if and only if In this study, we investigate some basic properties of the graph . In particular, we investigate some properties of , where is the ring of matrices over Also, we study the diameter of the bipartite graph associated to the quaternion ring
Some Properties of Cartesian Product of Non-Coprime Graph Associated with Finite Group Bawana, Agista Surya; Qonita, Niswah; Syarifudin, Abdul Gazir; Susanti, Yeni
Journal of the Indonesian Mathematical Society Vol. 31 No. 4 (2025): DECEMBER
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.v31i4.2095

Abstract

This paper investigates several properties of the Cartesian product of two non-coprime graphs associated with finite groups. Specifically, we focus on key numerical invariants, namely the domination number, independence number, and diameter. The non-coprime graph associated with finite group $G$ is constructed with the vertex set $G\setminus \{e\}$ and connects two distinct vertices if and only if their orders are not coprime. Using this construction, we investigate the Cartesian products of non-coprime graphs associated with various types of groups, including nilpotent groups, dihedral groups, and $p$-groups. We derive several new results, including exact expressions for the domination number, independence number, and diameter of these Cartesian products.
Co-Authors Abdul Gazir Syarifudin Bawana, Agista Surya Muhammad, Hubbi Wahyu Fibriyanti, R A Yeni Susanti