Zero divisor graphs of classes of five radical zero commutative completely primary finite rings

Abstract

This paper provides a characterization for zero divisor graphs of a completely primary finite ring R satisfying the conditions (Z (R))5 = (0) ; (Z (R))4 ̸= (0) where Z(R) is its subset of all zero divisors (including zero). This has been achieved through Anderson and Livingston’s zero divisor graphs by precisely determining the graph invariants, including diameter, girth and the binding number, and graph characteristics including completeness, connectedness and partiteness.