The Inclusion Ideal Graph of Rings

REFERENCES

• Akbari , S. , Kiani , D. , Mohammadi , F. , Moradi , S. ( 2009 ). The total graph and regular graph of a commutative ring . J. Pure Appl. Algebra 213 : 2224 – 2228 .
   Web of Science ®Google Scholar
• Akbari , S. , Habibi , M. , Majidinya , A. , Manaviyat , R. ( 2013 ). A note on comaximal graph of non-commutative rings . Algebr. Represent. Theory 16 ( 2 ): 303 – 307 .
   Web of Science ®Google Scholar
• Akbari , S. , Habibi , M. , Majidinya , A. , Manaviyat , R. ( 2013 ). On the idempotent graph of a ring . J. Algebra Appl. 12 ( 6 ): 13500003 , 14pgs .
   Web of Science ®Google Scholar
• Anderson , D. , Badawi , A. ( 2008 ). The total graph of a commutative ring . J. Algebra 320 : 2706 – 2719 .
   Web of Science ®Google Scholar
• Chakrabarty , I. , Ghosh , S. , Mukherjee , T. K. , Sen , M. K. ( 2009 ). Intersection graphs of ideals of rings . Discrete Math. 309 : 5381 – 5392 .
   Web of Science ®Google Scholar
• Chudnovsky , M. , Robertson , N. , Seymour , P. , Thomas , R. ( 2006 ). The strong perfect graph theorem . Annals of math. 1 ( 164 ): 51 – 229 .
   Google Scholar
• Cvetko-Vah , K. , Dolzan , D. ( 2008 ). Indecomposability graphs of rings . Bull. Aust. Math. Soc. 77 : 151 – 159 .
   Web of Science ®Google Scholar
• Hungerford , T. W. ( 1974 ). Algebra . New York : Springer-Verlag .
   Google Scholar
• Jacobson , N. ( 1964 ). Lectures in Abstract Algebra, Vol. 2. Linear Algebra. Princeton, NJ: Van Nostard .
   Google Scholar
• Kelarev , A. V. ( 1998 ). Directed graphs and nilpotent rings . J. Austral. Math. Soc. 65 : 326 – 332 .
   Web of Science ®Google Scholar
• Kelarev , A. V. ( 2002 ). Ring Constructions and Applications . Series Algebra : World Scientific .
   Google Scholar
• Kelarev , A. V. ( 2005 ). Directed graphs and Lie superalgebras of matrices . J. Algebra 285 : 1 – 10 .
   Web of Science ®Google Scholar
• Kelarev , A. V. , Passman , D. S. (2008). A description of incidence rings of group automata. Contemporary Mathematics 456:27–33.
   Google Scholar
• Lam , T. Y. ( 2001 ). A First Course in Noncommutative Rings . New York : Springer-Verlag .
   Google Scholar
• Lu , D. , Wu , T. ( 2009 ). On bipartite zero-divisor graphs . Discrete Math. 309 : 755 – 762 .
   Web of Science ®Google Scholar
• Redmond , S. ( 2007 ). On zero-divisor graphs of small finite commutative rings . Discrete Math. 307 : 1155 – 1166 .
   Web of Science ®Google Scholar
• Rédei , L. ( 1934 ). Ein kombinatorischer Satz . Acta. Litt. Sci. Szeged 7 : 39 – 43 .
   Google Scholar
• Wang , H. J. ( 2008 ). Graphs associated to co-maximal ideals of commutative rings . J. Algebra 320 : 2917 – 2933 .
   Web of Science ®Google Scholar
• Wu , T. , Liu , Q. , Chen , L. ( 2009 ). Zero-divisor semigroups and refinements of a star graph . Discrete Math. 309 : 2510 – 2518 .
   Web of Science ®Google Scholar
• Communicated by M. Bresar.
   Google Scholar