On Realizing Zero-Divisor Graphs

REFERENCES

• Akbari , S. , Mohammadian , A. ( 2004 ). On the zero-divisor graph of a commutative ring . J. Algebra 274 : 847 – 855 .
   Web of Science ®Google Scholar
• Anderson , D. F. , Livingston , P. S. ( 1999 ). The zero-divisor graph of a commutative ring . J. Algebra 217 : 434 – 447 .
   Web of Science ®Google Scholar
• Anderson , D. F. , Mulay , S. B. ( 2007 ). On the diameter and girth of a zero-divisor graph . J. Pure Appl. Algebra 210 : 543 – 550 .
   Web of Science ®Google Scholar
• Anderson , D. F. , Frazier , A. , Lauve , A. , Livingston , P. S. ( 2001 ). The Zero-Divisor Graph of a Commutative ring, II . Lecture Notes in Pure and Applied Mathematics , Vol. 220 . New York, Basel : Marcel Dekker , pp. 61 – 72 .
   Google Scholar
• Anderson , D. F. , Levy , R. , Shapiro , J. ( 2003 ). Zero-divisor graphs, von Neumann regular rings, and Boolean algebras . J. Pure Appl. Algebra 180 : 221 – 241 .
   Web of Science ®Google Scholar
• Axtel , M. , Coykendall , J. , Stickles , J. ( 2005 ). Zero-divisor graphs of polynomial and power series over commutative rings . Comm. Algebra 33 ( 6 ): 2043 – 2050 .
   Web of Science ®Google Scholar
• Beck , I. ( 1988 ). Coloring of commutative rings . J. Algebra 116 : 208 – 226 .
   Web of Science ®Google Scholar
• DeMeyer , F. , Schneider , K. ( 2002 ). Automorphisms and zero-divisor graphs of commutative rings . Internat. J. Commutative Rings 1 ( 3 ): 93 – 106 .
   Google Scholar
• Grätzer , G. ( 1978 ). General Lattice Theory . Basel : Birkhäuser Verlag .
   Google Scholar
• LaGrange , J. D. ( 2007 ). Complemented zero-divisor graphs and Boolean rings . J. Algebra 315 : 600 – 611 .
   Web of Science ®Google Scholar
• Levy , R. , Shapiro , J. ( 2002 ). The zero-divisor graph of von Neumann regular rings . Comm. Algebra 30 ( 2 ): 745 – 750 .
   Web of Science ®Google Scholar
• Lucas , T. G. ( 2006 ). The diameter of a zero divisor graph . J. Algebra 301 : 174 – 193 .
   Web of Science ®Google Scholar
• Mulay , S. B. ( 2002 ). Cycles and symmetries of zero-divisors . Comm. Algebra 30 ( 7 ): 3533 – 3558 .
   Web of Science ®Google Scholar
• Redmond , S. P. ( 2007 ). On zero-divisor graphs of small finite commutative rings . Discrete Math. 307 : 1155 – 1166 .
   Web of Science ®Google Scholar
• Smith , N. O. ( 2003 ). Planar zero-divisor graphs . Internat. J. Commutative Rings 2 : 177 – 188 .
   Google Scholar
• Communicated by I. Swanson.
   Google Scholar