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2012 Diameter, girth and cut vertices of the graph of equivalence classes of zero-divisors
Blake Allen, Erin Martin, Eric New, Dane Skabelund
Involve 5(1): 51-60 (2012). DOI: 10.2140/involve.2012.5.51

Abstract

We explore the properties of ΓE(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 Γ(R) and the equivalence class graph ΓE(R), and examine properties of cut-vertices of ΓE(R).

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Blake Allen. Erin Martin. Eric New. Dane Skabelund. "Diameter, girth and cut vertices of the graph of equivalence classes of zero-divisors." Involve 5 (1) 51 - 60, 2012. https://doi.org/10.2140/involve.2012.5.51

Information

Received: 19 January 2011; Revised: 2 August 2011; Accepted: 18 August 2011; Published: 2012
First available in Project Euclid: 20 December 2017

zbMATH: 1246.13007
MathSciNet: MR2924313
Digital Object Identifier: 10.2140/involve.2012.5.51

Subjects:
Primary: 13A99

Rights: Copyright © 2012 Mathematical Sciences Publishers

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