Table of Contents
International Journal of Combinatorics
Volume 2012 (2012), Article ID 957284, 13 pages
http://dx.doi.org/10.1155/2012/957284
Research Article

On the Line Graph of the Zero Divisor Graph for the Ring of Gaussian Integers Modulo

1Department of Mathematics, Palestine Technical University-Kadoorie, P.O. Box 7 Tulkarm, West Bank, Palestine
2Department of Mathematics, Irbid National University, P.O. Box 2600 Irbid, 21110, Jordan

Received 9 September 2011; Accepted 26 December 2011

Academic Editor: Gelasio Salazar

Copyright © 2012 Khalida Nazzal and Manal Ghanem. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. I. Beck, “Coloring of commutative rings,” Journal of Algebra, vol. 116, no. 1, pp. 208–226, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. D. F. Anderson and P. S. Livingston, “The zero-divisor graph of a commutative ring,” Journal of Algebra, vol. 217, no. 2, pp. 434–447, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. D. F. Anderson, A. Frazier, A. Lauve, and P. S. Livingston, “The zero-divisor graph of a commutative ring. II,” in Ideal Theoretic Methods in Commutative Algebra, vol. 220 of Lecture Notes in Pure and Applied Mathematics, pp. 61–72, Marcel Dekker, New York, NY, USA, 2001. View at Google Scholar · View at Zentralblatt MATH
  4. S. Akbari and A. Mohammadian, “On the zero-divisor graph of a commutative ring,” Journal of Algebra, vol. 274, no. 2, pp. 847–855, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. D. F. Anderson and A. Badawi, “On the zero-divisor graph of a ring,” Communications in Algebra, vol. 36, no. 8, pp. 3073–3092, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. N. Cordova, C. Gholston, and H. Hauser, The Structure of Zero-Divisor Graphs, Summer Undergraduate Mathematical Sciences Research Institute, Miami University, 2005.
  7. A. Duane, “Proper Coloring and p-partite structures of the zero-divisor graph,” Rose-Hulman Undergraduate Mathematics Journal, vol. 7, no. 2, pp. 1–7, 2006. View at Google Scholar
  8. V. K. Bhat, R. Raina, N. Nehra, and O. Prakash, “A note on zero divisor graph over rings,” International Journal of Contemporary Mathematical Sciences, vol. 2, no. 13–16, pp. 667–671, 2007. View at Google Scholar · View at Zentralblatt MATH
  9. P. F. Lee, Line graph of zero divisor graph in commutative rings, M.S. thesis, Colorado Christian University, 2007.
  10. A. Phillips, J. Rogrers, K. Tolliver, and F. Worek, Uncharted Territory of Zero-Divisor Graphs and Their Complements, Summer Undergraduate Mathematical Science Research Institute, Miami University, 2004.
  11. E. Abu Osba, S. Al-Addasi, and N. Abu Jaradeh, “Zero divisor graph for the ring of Gaussian integers modulo n,” Communications in Algebra, vol. 36, no. 10, pp. 3865–3877, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. E. Abu Osba, S. Al-Addasi, and B. Al-Khamaiseh, “Some properties of the zero-divisor graph for the ring of Gaussian integers modulo n,” Glasgow Mathematical Journal, vol. 53, no. 2, pp. 391–399, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. H. J. Veldman, “A result on Hamiltonian line graphs involving restrictions on induced subgraphs,” Journal of Graph Theory, vol. 12, no. 3, pp. 413–420, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. S. Skiena, Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica, Addison-Wesley, Redwood City, Calif, USA, 1990.
  15. J. Sedláček, “Some properties of interchange graphs,” in Theory of Graphs and its Application, pp. 145–150, Academic Press, New York, NY, USA, 1962. View at Google Scholar · View at Zentralblatt MATH
  16. S. P. Redmond, “Central sets and radii of the zero-divisor graphs of commutative rings,” Communications in Algebra, vol. 34, no. 7, pp. 2389–2401, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  17. S. Arumugam and S. Velammal, “Edge domination in graphs,” Taiwanese Journal of Mathematics, vol. 2, no. 2, pp. 173–179, 1998. View at Google Scholar · View at Zentralblatt MATH