A Graded Zero‐Divisor Graph Arising From Group‐Graded Modules

In this paper, we introduce a graded zero‐divisor graph for group‐graded modules, where the vertices are homogeneous elements and edges connect distinct vertices according to a natural graded relation. We investigate its main properties, such as connectivity and girth, and compare these graphs with their ungraded counterparts. Additionally, we correct several previously reported results in the graded setting. Our findings extend and generalize earlier work and include several nontrivial new results.