×

Diameter, girth and cut vertices of the graph of equivalence classes of zero-divisors. (English) Zbl 1246.13007

Summary: We explore the properties of \(\Gamma_E(R)\), the graph of equivalence classes of zero-divisors of a commutative Noetherian ring \(R\). We determine the possible combinations of diameter and girth for the zero-divisor graph \(\Gamma(R)\) and the equivalence class graph \(\Gamma_E(R)\), and examine properties of cut-vertices of \(\Gamma_E(R)\).

MSC:

13A99 General commutative ring theory
PDFBibTeX XMLCite
Full Text: DOI Link