Table of Contents
International Journal of Combinatorics
Volume 2014, Article ID 348359, 13 pages
http://dx.doi.org/10.1155/2014/348359
Research Article

Bounds on the Size of the Minimum Dominating Sets of Some Cylindrical Grid Graphs

1Department of Statistics, West Bengal State University, Barasat, North 24 Parganas 700126, India
2IMBIC, AH 317, Salt Lake City, Calcutta 700091, India
3Department of Pure Mathematics, University of Calcutta, 35 Ballygunge Circular Road, Calcutta 700019, India

Received 30 August 2013; Accepted 23 January 2014; Published 7 April 2014

Academic Editor: Liying Kang

Copyright © 2014 Mrinal Nandi 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. T. Haynes, S. Hedetniemi, and P. Slater, Fundamentals of Domination in Graphs, Marcel Dekker, New York, NY, USA, 1998.
  2. J. E. Dunbar, S. T. Hedetniemi, M. A. Henning, and P. J. Slater, “Signed domination in graphs,” in Graph Theory, Combinatorics and Applications, pp. 311–322, John Wiley & Sons, 1995. View at Google Scholar · View at Zentralblatt MATH
  3. O. Favaron, “Signed domination in regular graphs,” Discrete Mathematics, vol. 158, no. 1–3, pp. 287–293, 1996. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  4. O. Morgenstern, “The colaboration between Oskar Morgenstern and John von Neumann on the theory of games,” Journal of Economic Literature, vol. 14, pp. 805–816, 1976. View at Google Scholar
  5. S. T. Hedetniemi and R. C. Laskar, “Bibliography on domination in graphs and some basic definitions of domination parameters,” Discrete Mathematics, vol. 86, no. 1–3, pp. 257–277, 1990. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  6. V. G. Vizing, “The cartesian product of graphs,” Vychisl Sistemy, vol. 9, pp. 30–43, 1963. View at Google Scholar
  7. S. Gravier, “Total domination number of grid graphs,” Discrete Applied Mathematics, vol. 121, no. 1–3, pp. 119–128, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  8. R. J. Faudree and R. H. Schelp, “The domination number for the product of graphs,” Congressus Numerantium, vol. 79, pp. 29–33, 1990. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. M. El-Zahar and C. M. Pareek, “Domination number of products of graphs,” Ars Combinatoria, vol. 31, pp. 223–227, 1991. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. F. Harary, Graph Theory, Addison-Weslay, Reading, Mass, USA, 1969.
  11. S. Klavžar and N. Seifter, “Dominating cartesian products of cycles,” Discrete Applied Mathematics, vol. 59, no. 2, pp. 129–136, 1995. View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  12. B. N. Clark, C. J. Colbourn, and D. S. Johnson, “Unit disk graphs,” Discrete Mathematics, vol. 86, no. 1–3, pp. 165–177, 1990. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  13. M. S. Jacobson and L. F. Kinch, “On the domination of the products of graphs I,” Ars Combinatoria, vol. 18, pp. 33–44, 1983. View at Google Scholar
  14. T. Y. Chang and W. E. Clark, “The domination numbers of the 5×n and 6×n grid graphs,” Journal of Graph Theory, vol. 17, pp. 81–107, 1993. View at Google Scholar
  15. M. H. El-Zahar, S. M. Khamis, and K. M. Nazzal, “On the domination number of the cartesian product of the cycle of length n and any graph,” Discrete Applied Mathematics, vol. 155, no. 4, pp. 515–522, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  16. B. L. Hartnell and D. F. Rall, “On Vizing’s conjecture,” Congressus Numerantium, vol. 82, pp. 87–96, 1991. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. M. Nandi, S. Parui, and A. Adhikari, “Domination number of cylindrical grids,” Applied Mathematics and Computation, vol. 217, no. 10, pp. 4879–4889, 2011. View at Publisher · View at Google Scholar · View at Scopus
  18. G. J. Pottie and W. J. Kaiser, “Wireless integrated network sensors,” Communications of the ACM, vol. 43, no. 5, pp. 51–58, 2000. View at Google Scholar · View at Scopus
  19. C. Farah, F. Schwaner, A. Abedi, and M. Worboys, “Distributed homology algorithm to detect topological events via wireless sensor networks,” IET Wireless Sensor Systems, vol. 1, no. 3, pp. 151–160, 2011. View at Publisher · View at Google Scholar · View at Scopus
  20. F. Martincic and L. Schwiebert, “Introduction to wireless sensor networking,” in Handbook of Sensor Networks: Algorithms and Architectures, I. Stojmenovic, Ed., chapter 1, John Wiley & Sons, 2005. View at Google Scholar
  21. X. Bai, S. Kumar, D. Xuan, Z. Yun, and T. H. Lai, “Deploying wireless sensors to achieve both coverage and connectivity,” in Proceedings of the 7th ACM International Symposium on Mobile Ad Hoc Networking and Computing (MOBIHOC '06), pp. 131–142, May 2006. View at Scopus