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On domination numbers of zero-divisor graphs of commutative rings.
- Source :
- Electronic Journal of Graph Theory & Applications; 2024, Vol. 12 Issue 2, p169-180, 12p
- Publication Year :
- 2024
-
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]
- Subjects :
- COMMUTATIVE rings
Subjects
Details
- Language :
- English
- ISSN :
- 23382287
- Volume :
- 12
- Issue :
- 2
- Database :
- Complementary Index
- Journal :
- Electronic Journal of Graph Theory & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 180665967
- Full Text :
- https://doi.org/10.5614/ejgta.2024.12.2.2