On domination numbers of zero-divisor graphs of commutative rings

Zero-divisor graphs of a commutative ring R, denoted Gamma(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 Gamma(R) when the sum of the domination numbers of Gamma(R) and the complement of Gamma(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.