### TOTAL GRAPH AND COMPLEMENTED GRAPH OF A ROUGH SEMIRING

#### Abstract

*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

#### Full Text:

PDF#### 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.