On domination numbers of zero-divisor graphs of commutative rings - Anderson, Sarah E.; Axtell, Mike; Kroschel, Brenda K.; Stickles, Jr., Joe A. (Electronic Journal of Graph Theory and Applications (EJGTA), 2024)
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.