Allen, Blake; Martin, Erin; New, Eric; Skabelund, Dane Diameter, girth and cut vertices of the graph of equivalence classes of zero-divisors. (English) Zbl 1246.13007 Involve 5, No. 1, 51-60 (2012). 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 \(\Gamma_E(R)\). Cited in 5 Documents MSC: 13A99 General commutative ring theory Keywords:zero-divisor graph; diameter; girth; cut vertices PDFBibTeX XMLCite \textit{B. Allen} et al., Involve 5, No. 1, 51--60 (2012; Zbl 1246.13007) Full Text: DOI Link