The unit-zero divisor graph of a commutative ring

In this paper, we propose a new graph construction associated with a commutative ring with identity. Let [Formula: see text] be such a ring. We define the unit-zero divisor graph of [Formula: see text], denoted by [Formula: see text], whose vertex set is [Formula: see text]. Two distinct vertices [Formula: see text] and [Formula: see text] are adjacent if and only if [Formula: see text] is a unit in [Formula: see text] and [Formula: see text] is a zero divisor. This combined adjacency condition incorporates both additive and multiplicative structures of the ring, resulting in a graph that simultaneously reflects these two operations. We investigate several fundamental properties of [Formula: see text], including regularity, bipartiteness, planarity, and Hamiltonicity. Moreover, we analyze how these graph-theoretic properties are governed by algebraic components of the ring, such as the group of units, the zero divisor set, ideals, and the Jacobson radical.