Table of Contents
International Journal of Combinatorics
Volume 2014, Article ID 952371, 6 pages
http://dx.doi.org/10.1155/2014/952371
Research Article

Some Properties of the Intersection Graph for Finite Commutative Principal Ideal Rings

1Department of Mathematics, The University of Jordan, Amman 11942, Jordan
2Department of Mathematics, Hashemite University, Zarqa 13115, Jordan

Received 28 May 2014; Accepted 10 September 2014; Published 25 September 2014

Academic Editor: Johannes Hendrik Hattingh

Copyright © 2014 Emad Abu Osba et al. 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. R. Wilson, Introduction to Graph Theory, Pearson Prentice Hall, Kuala Lumpur, Malaysia, 4th edition, 1996.
  2. E. Abu Osba, “The intersection graph for finite commutative principal ideal rings,” Submitted.
  3. J. Bosak, “The graphs of semigroups,” in Theory of Graphs and Application, pp. 119–125, Academic Press, New York, NY, USA, 1964. View at Google Scholar
  4. I. Chakrabarty, S. Ghosh, T. K. Mukherjee, and M. K. Sen, “Intersection graphs of ideals of rings,” Discrete Mathematics, vol. 309, no. 17, pp. 5381–5392, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. B. Csákéany and G. Pollák, “The graph of subgroups of a finite group,” Czechoslovak Mathematical Journal, vol. 19, pp. 241–247, 1969. View at Google Scholar · View at MathSciNet
  6. S. H. Jafari and N. J. Rad, “Planarity of intersection graphs of ideals of rings,” International Electronic Journal of Algebra, vol. 8, pp. 161–166, 2010. View at Google Scholar · View at MathSciNet
  7. B. Zelinka, “Intersection graphs of finite abelian groups,” Czechoslovak Mathematical Journal, vol. 25, no. 2, pp. 171–174, 1975. View at Google Scholar · View at MathSciNet
  8. B. R. McDonald, Finite Rings with Identity, Marcel Dekker, New York, NY, USA, 1974. View at MathSciNet
  9. T. Hungerford, Algebra, Springer, New York, NY, USA, 8th edition, 1996. View at MathSciNet
  10. M. F. Atiyah and I. G. Macdonald, Introduction to Commutative Algebra, Addison-Wesley, London, UK, 1969. View at MathSciNet
  11. G. Chartrand, F. Harary, and P. Zhang, “On the geodetic number of a graph,” Networks, vol. 39, no. 1, pp. 1–6, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. C. Hernando, T. Jiang, M. Mora, I. M. Pelayo, and C. Seara, “On the Steiner, geodetic and hull numbers of graphs,” Discrete Mathematics, vol. 293, no. 1–3, pp. 139–154, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. S. Spiroff and C. Wickham, “A zero divisor graph determined by equivalence classes of zero divisors,” Communications in Algebra, vol. 39, no. 7, pp. 2338–2348, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus