On domination numbers of zero-divisor graphs of commutative rings

Zero-divisor graphs of a commutative ring R , denoted Γ( R ) , are well-represented in the literature. In this paper, we consider domination numbers of zero-divisor graphs. For reduced rings, Vatandoost and Ramezani characterized the possible graphs for Γ( R ) when the sum of the domination numbers of Γ( R ) and the complement of Γ( R ) is n - 1 , n , and n + 1 , where n is the number of nonzero zero-divisors of R . We extend their results to nonreduced rings, determine which graphs are realizable as zero-divisor graphs, and provide the rings that yield these graphs.