The Total Graph of a Commutative Semiring

[1] D. D. Anderson and M. Naseer, Beck's coloring of a commutative ring, J. Algebra, 159 (1993), 500-514.10.1006/jabr.1993.1171Search in Google Scholar

[2] D. F. Anderson and A. Badawi, The total graph of a commutative ring, J. Algebra, 320 (2008), 2706-2719.10.1016/j.jalgebra.2008.06.028Search in Google Scholar

[3] D. F. Anderson and P. F. Livingston, The zero-divisor graph of a com- mutative ring, J. Algebra, 217 (1999), 437-447.10.1006/jabr.1998.7840Search in Google Scholar

[4] P. J. Allen, A fundamental theorem of homomorphisms for semirings, Proc. Amer. Math. Soc. 21 (1969), 412-416.10.1090/S0002-9939-1969-0237575-4Search in Google Scholar

[5] I. Beck, Coloring of a commutative ring, J. Algebra, 116 (1988), 208-226.10.1016/0021-8693(88)90202-5Search in Google Scholar

[6] S. Ebrahimi Atani, The ideal theory in quotients of commutative semir- ings, Glas. Math., 42 (2007), 301-308.10.3336/gm.42.2.05Search in Google Scholar

[7] S. Ebrahimi Atani, The zero-divisor graph with respect to ideals of a com- mutative semiring, Glas. Math., 43 (2008), 309-320.10.3336/gm.43.2.06Search in Google Scholar

[8] S. Ebrahimi Atani, An ideal-based zero-divisor graph of a commutative semiring, Glas. Math., 44 (1) (2009), 141-153.10.3336/gm.44.1.07Search in Google Scholar

[9] S. Ebrahimi Atani and R. Ebrahimi Atani, Some remarks on partitioning semirings, An. St. Univ. Ovidius Constanta, 18(1) (2010), 49-62.Search in Google Scholar

[10] S. Ebrahimi Atani and S. Habibi, The total torsion element graph of a module over a commutative ring, An. St. Univ. Ovidius Constanta, 19(1) (2011), 23-34.Search in Google Scholar

[11] J. S. Golan, The theory of semirings with applications in mathematics and theoretical computer Science, Pitman Monographs and Surveys in Pure and Applied Mathematics, Longman Scientific and Technical, Harlow UK, (1992).Search in Google Scholar

[12] J. S. Golan, Semirings and their Applications, Kluwer Academic Publish- ers, Dordrecht, (1999).10.1007/978-94-015-9333-5Search in Google Scholar

[13] S. B. Mulay, Cycles and symmetries of zero-divisors, Comm. Algebra, 30(7) (2002), 3533-3558. 10.1081/AGB-120004502Search in Google Scholar