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Communications in Algebra Volume 38, 2010 - Issue 8
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Original Articles

Local Rings with Genus Two Zero Divisor Graph

Nathan Bloomfield Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas, USACorrespondence[email protected]
&
Cameron Wickham Department of Mathematics, Missouri State University, Springfield, Missouri, USA
Pages 2965-2980 | Received 17 Nov 2008, Published online: 18 Aug 2010

REFERENCES

  • Anderson , D. F. , Livingston , P. S. ( 1999 ). The zero-divisor graph of a commutative ring . J. Algebra 217 : 434 – 447 .
  • Archdeacon , D. ( 1996 ). Topological graph theory: a survey . Cong. Num. 115 : 115 – 5 .
  • Beck , I. ( 1988 ). Coloring of commutative rings . J. Algebra 116 : 208 – 226 .
  • Belshoff , R. , Chapman , J. ( 2007 ). Planar zero-divisor graphs . J. Algebra 316 : 471 – 480 .
  • Bini , G. , Flamini , F. ( 2002 ). Finite Commutative Rings and Their Applications . Norwell , MA : Kluwer Academic Publishers .
  • Corbas , B. , Williams , G. D. ( 2000 ). Rings of order P 5 part I: nonlocal rings . J. Algebra 231 : 677 – 690 .
  • Corbas , B. , Williams , G. D. ( 2000 ). Rings of order p 5 part II: local rings . J. Algebra 231 : 691 – 704 .
  • Ellingham , M. N. , Stephens , D. C. ( 2009 ). The orientable genus of some joins of complete graphs with large edgeless graphs . Discrete Math. 309 ( 5 ): 1190 – 1198 .
  • Howie , J. M. ( 1976 ). An Introduction to Semigroup Theory . University of Michigan : Academic Press .
  • Wang , H.-j ( 2006 ). Zero divisor graphs of genus one . J. Algebra 304 ( 2 ): 666 – 678 .
  • Mohar , B. , Thomassen , C. ( 2001 ). Graphs on Surfaces . Baltimore , MD : Johns Hopkins .
  • Smith , N. O. ( 2002 ). Planar zero-divisor graphs . Int. J. Comm. Rings. 2 ( 4 ): 177 – 188 .
  • Thomassen , C. ( 1989 ). The graph genus problem is NP-complete . J. Algorithms 10 ( 4 ): 568 – 576 .
  • Wickham , C. ( 2008 ). Classification of rings with genus one zero-divisor graphs . Comm. Algebra 36 ( 2 ): 325 – 345 .
  • Wickham , C. ( 2209 ). Rings whose zero-divisor graphs have positive genus . J. Algebra 321 ( 2 ): 377 – 383 .
  • Communicated by I. Swanson.

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