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Diameter, girth
and cut vertices of the graph of equivalence classes of
zero-divisors
Blake Allen, Erin Martin, Eric New and Dane Skabelund
Vol. 5 (2012), No. 1, 51–60
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Abstract |
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We explore the properties of , the graph of equivalence classes of zero-divisors of a commutative Noetherian ring . We determine the possible combinations of diameter and girth for the zero-divisor graph and the equivalence class graph , and examine properties of cut-vertices of . |
Keywords
zero-divisor graph, diameter, girth, cut vertices
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Mathematical Subject Classification 2010
Primary: 13A99
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Milestones
Received: 19 January 2011
Revised: 2 August 2011
Accepted: 18 August 2011
Published: 28 April 2012
Communicated by Scott Chapman
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Authors |
| Blake Allen | |
| Department of Mathematics Utah Valley University Orem, UT 84058 United States |
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| Erin Martin | |
| Department of Physics and
Mathematics William Jewell College Liberty, MO 64068 United States |
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| Eric New | |
| Department of Mathematics and
Statistics The College of New Jersey Ewing, NJ 08628 United States |
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| Dane Skabelund | |
| Department of Mathematics Brigham Young University Provo, UT 84602 United States |
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