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

Key Points

• The main aim is to introduce and analyze the properties of graded zero-divisor graphs associated with group-graded modules.
• Define a graded zero-divisor graph with homogeneous vertex elements.
• Establish edges based on a natural graded relation between distinct vertices.
• Examine properties such as connectivity and girth.
• Compare graded graphs with ungraded versions.
• Identified key properties of graded zero-divisor graphs, like their connectivity and girth.
• Corrected several previously reported findings in the graded context.
• Extended prior work, resulting in notable new insights into the structure of these graphs.