On the Unit-Jacobson Graph

In this paper, we introduce the unit-Jacobson graph, which is defined by the unit elements and the elements of the Jacobson radical of a commutative ring Formula: see text with nonzero identity. We give relationships between this new graph concept and some special rings such as Formula: see text-clean rings, Formula: see text-rings, local rings, and cartesian rings. Moreover, we investigate the concepts of the dominating set, diameter, and girth on the unit-Jacobson graph.