The matrix Jacobson graph of finite commutative rings
| Main Authors: | Humaira, Siti; Bandung Institute of Technology, Astuti, Pudji; Algebra Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia, Muchtadi-Alamsyah, Intan; Algebra Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia, Erfanian, Ahmad; Department of Pure Mathematics and the Center of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad, Mashhad, Iran |
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| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB
, 2022
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| Subjects: | |
| Online Access: |
https://www.ejgta.org/index.php/ejgta/article/view/1388 https://www.ejgta.org/index.php/ejgta/article/view/1388/pdf_212 |
Daftar Isi:
- The notion of the matrix Jacobson graph was introduced in 2019. Let R be a commutative ring and J(R) be the Jacobson radical of ring R. The matrix Jacobson graph of ring R size m × n, denoted J(R)m × n, is defined as a graph where the vertex set is Rm × n ∖ J(R)m × n such that two distinct vertices A, B are adjacent if and only if 1 − det(AtB) is not a unit in ring R. Here we obtain some graph theoretical properties of J(R)m × n including its connectivity, planarity and perfectness.