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On domination numbers of zero-divisor graphs of commutative rings.

Authors :
Anderson, Sarah E.
Axtell, Michael C.
Kroschel, Brenda K.
Stickles Jr., Joe A.
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

Subjects :
COMMUTATIVE rings

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