The matrix Jacobson graph of finite commutative rings - Siti Humaira; Pudji Astuti; Intan Muchtadi-Alamsyah; Ahmad Erfanian (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2022)
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.