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Five-point
zero-divisor graphs determined by equivalence classes
Florida Levidiotis and Sandra Spiroff
Vol. 4 (2011), No. 1, 53–64
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Abstract |
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We study condensed zero-divisor graphs (those whose vertices are equivalence classes of zero-divisors of a ring ) having exactly five vertices. In particular, we determine which graphs with exactly five vertices can be realized as the condensed zero-divisor graph of a ring. We provide the rings for the graphs which are possible, and prove that the rest of graphs can not be realized via any commutative ring. There are 34 graphs in total which contain exactly five vertices. |
Keywords
condensed zero-divisor graphs, equivalence classes of
zero-divisors
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Mathematical Subject Classification 2000
Primary: 13A99
Secondary: 05C99
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Milestones
Received: 17 June 2010
Revised: 11 February 2011
Accepted: 23 February 2011
Published: 22 September 2011
Communicated by Scott Chapman
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Authors |
| Florida Levidiotis | |
| Department of Mathematics and
Statistics Loyola University Chicago 26 E Pearson Street, #2305 Chicago, IL 60611 United States |
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| Sandra Spiroff | |
| Department of Mathematics University of Mississippi Hume Hall 305 P.O. Box 1848 University, MS 38677-1848 United States |
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| http://home.olemiss.edu/depts/mathematics/spiroff.htm | |
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