1. On domination numbers of zero-divisor graphs of commutative rings.
- Author
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Anderson, Sarah E., Axtell, Michael C., Kroschel, Brenda K., and Stickles Jr., Joe A.
- Subjects
COMMUTATIVE rings - Abstract
Zero-divisor graphs of a commutative ring R, denoted G(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 G(R) when the sum of the domination numbers of G(R) and the complement of G(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. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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