In this paper, we examine the algebraic properties of localizations of commutative rings and how localizations affect the zero-divisor graphs structure of modular rings. We also classify the zero-divisor graphs of modular rings with respect to both the diameter and girth of their resultant zero-divisor graphs.
Cuchta, Thomas; Lokken, Kathryn A.; and Young, William
"Zero-divisor Graphs of Localizations and Modular Rings,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 9:
2, Article 3.
Available at: https://scholar.rose-hulman.edu/rhumj/vol9/iss2/3