TOTAL GRAPH AND COMPLEMENTED GRAPH OF A ROUGH SEMIRING

Year 2016, Volume: 29 Issue: 2, 459 - 466, 21.06.2016

A. Manimaran , B. Praba V. M. Chandrasekaran

Abstract

      In this paper, we define the Total graph and the complemented graph of a rough semiring (T, ∆, ∇). We prove that the existence theorem of the total graph and the complemented graph on (T, ∆, ∇) for X ⊆ U where U is the finite universal set on the set of all rough sets for the given information system I = (U, A) together with the operations praba ∆ and praba ∇. We illustrate these concepts through examples.

Keywords

Semiring, Zero divisor, Zero divisor graph, Rough Semiring

Semiring

Abstract

References

• References
• S. Akbari and A. Mohammadian, On the Zero Divisor Graph of a Commutative Ring, Journal of Algebra,
• (2004), 847-855.
• D. F. Anderson and P.S. Livingston, The Zero Divisor Graph of a Commutative Ring, Journal of Algebra,
• (2) (1999), 434-437.
• D. F. Anderson and A. Badawi, The Total Graph of a Commutative Ring, Journal of Algebra, 320
• (2008), 2706-2719.
• D. D. Anderson and M. Naseer, Beck’s Coloring of a Commutative Ring, Journal of Algebra, 159(2)
• (1993), 500-514.
• I. Beck, Coloring of a Commutative Ring, Journal of Algebra, 116(1) (1988),208-226.
• David Dolzan and Polana Oblak, The Zero Divisor Graphs of Rings and Semirings, International Journal of Algebra and Computation, 22(4)(2012).
• S. Ebrahimi Atani, The Zero Divisor Graph With Respect to Ideals of a Commutative Semiring, Glass.Math., 43(2008), 309-320.
• S. Ebrahimi Atani, An Ideal Based Zero Divisor Graph of a Commutative Semiring, Glass. Math., 44(1)(2009), 141-153.
• A.Manimaran, B.Praba and V.M.Chandrasekaran, Regular Rough ∇ Monoid of idempotents,
• International Journal of Applied Engineering and Research,9(16)(2014),3469-3479
• A.Manimaran, B.Praba and V.M.Chandrasekaran, Characterization of Rough Semiring, Afrika
• Matemattika (Communicated).
• Z.Pawlak, Rough Sets, International Journal of Computer and Information Sciences, 11 (1982),341–356.
• B.Praba, R.Mohan, Rough Lattice, International Journal of Fuzzy Mathematics and
• System,3(2)(2013),135-151.
• B.Praba, V.M.Chandrasekaran and A.Manimaran, A Commutative Regular Monoid on Rough Sets,
• Italian Journal of Pure and Applied Mathematics, 31 (2013),307-318.
• B.Praba, V.M.Chandrasekaran and A.Manimaran, Semiring on Rough sets, Indian Journal of Science
• and Technology, 8(3) (2015), 280-286.
• B.Praba, A. Manimaran and V.M.Chandrasekaran,The Zero Divisor graph of a Rough Semiring,
• International Journal of Pure and Applied Mathematics, 98(5) (2015), 33-37.
• S. Visweswaran, Some Properties of the Complement of the Zero Divisor Graph of a Commutative
• Ring, International Scholar Research Network, 11 (2011), 24 pages.
• L.A.Zadeh, Fuzzy Sets, Information and Control, 8 (1965),338-353.