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TOTAL GRAPH AND COMPLEMENTED GRAPH OF A ROUGH SEMIRING

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

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.

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.

Semiring

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

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.
There are 29 citations in total.

Details

Journal Section Mathematics
Authors

A. Manimaran

B. Praba This is me

V. M. Chandrasekaran This is me

Publication Date June 21, 2016
Published in Issue Year 2016 Volume: 29 Issue: 2

Cite

APA Manimaran, A., Praba, B., & Chandrasekaran, V. M. (2016). TOTAL GRAPH AND COMPLEMENTED GRAPH OF A ROUGH SEMIRING. Gazi University Journal of Science, 29(2), 459-466.
AMA Manimaran A, Praba B, Chandrasekaran VM. TOTAL GRAPH AND COMPLEMENTED GRAPH OF A ROUGH SEMIRING. Gazi University Journal of Science. June 2016;29(2):459-466.
Chicago Manimaran, A., B. Praba, and V. M. Chandrasekaran. “TOTAL GRAPH AND COMPLEMENTED GRAPH OF A ROUGH SEMIRING”. Gazi University Journal of Science 29, no. 2 (June 2016): 459-66.
EndNote Manimaran A, Praba B, Chandrasekaran VM (June 1, 2016) TOTAL GRAPH AND COMPLEMENTED GRAPH OF A ROUGH SEMIRING. Gazi University Journal of Science 29 2 459–466.
IEEE A. Manimaran, B. Praba, and V. M. Chandrasekaran, “TOTAL GRAPH AND COMPLEMENTED GRAPH OF A ROUGH SEMIRING”, Gazi University Journal of Science, vol. 29, no. 2, pp. 459–466, 2016.
ISNAD Manimaran, A. et al. “TOTAL GRAPH AND COMPLEMENTED GRAPH OF A ROUGH SEMIRING”. Gazi University Journal of Science 29/2 (June 2016), 459-466.
JAMA Manimaran A, Praba B, Chandrasekaran VM. TOTAL GRAPH AND COMPLEMENTED GRAPH OF A ROUGH SEMIRING. Gazi University Journal of Science. 2016;29:459–466.
MLA Manimaran, A. et al. “TOTAL GRAPH AND COMPLEMENTED GRAPH OF A ROUGH SEMIRING”. Gazi University Journal of Science, vol. 29, no. 2, 2016, pp. 459-66.
Vancouver Manimaran A, Praba B, Chandrasekaran VM. TOTAL GRAPH AND COMPLEMENTED GRAPH OF A ROUGH SEMIRING. Gazi University Journal of Science. 2016;29(2):459-66.