The matrix Jacobson graph of finite commutative rings

Siti Humaira (Bandung Institute of Technology)
Pudji Astuti (Algebra Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia)
Intan Muchtadi-Alamsyah (Algebra Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia)
Ahmad Erfanian (Department of Pure Mathematics and the Center of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad, Mashhad, Iran)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 10, No 1 (2022): Electronic Journal of Graph Theory and Applications

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 ????(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 ????(R)m × n including its connectivity, planarity and perfectness.