The matrix Jacobson graph of finite commutative rings

The matrix Jacobson graph was introduced in 2019 as a generalization of Jacobson graph and n-array Jacobson graph. Let R be a commutative ring and J(R) be the Jacobson radical of the ring R. The matrix Jacobson graph of the ring R of size m x n, denoted by J(R)(mxn), is defined as a graph where the vertex set is R-mxn\J(R)mxn such that two distinct vertices A,B are adjacent if and only if 1-det(A(t)B) is not a unit in the ring R. Here we obtain some graph theoretical properties of J(R)(mxn) including its connectivity, planarity and perfectness.