Table of Contents Author Guidelines Submit a Manuscript
The Scientific World Journal
Volume 2014, Article ID 741932, 12 pages
http://dx.doi.org/10.1155/2014/741932
Research Article

-Labeling of the Strong Product of Paths and Cycles

1School of Information Science and Technology, Chengdu University, Chengdu 610106, China
2Key Laboratory of Pattern Recognition and Intelligent Information Processing, Institutions of Higher Education of Sichuan Province, Sichuan 610106, China
3Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška Cesta 160, 2000 Maribor, Slovenia

Received 21 September 2013; Accepted 24 October 2013; Published 24 February 2014

Academic Editors: Y. Wang and S. Xiang

Copyright © 2014 Zehui Shao and Aleksander Vesel. 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. J. Kratochvíl, D. Kratsch, and M. Liedloff, “Exact algorithms for L(2, 1)-labeling of graphs,” in Proceedings of the 32nd Mathematical Foundations of Computer Science (MFCS '07), pp. 513–524, 2007.
  2. L. M. San José-Revuelta, “A new adaptive genetic algorithm for fixed channel assignment,” Information Sciences, vol. 177, no. 13, pp. 2655–2678, 2007. View at Publisher · View at Google Scholar · View at Scopus
  3. G. J. Chang and D. Kuo, “The L(2, 1)-labeling problem on graphs,” SIAM Journal on Discrete Mathematics, vol. 9, no. 2, pp. 309–316, 1996. View at Google Scholar · View at Scopus
  4. J. R. Griggs and R. K. Yeh, “Labelling graphs with a condition at distance two,” SIAM Journal on Discrete Mathematics, vol. 5, pp. 586–595, 1992. View at Google Scholar
  5. H. L. Bodlaender, T. Kloks, R. B. Tan, and J. Van Leeuwen, “Approximations for λ-colorings of graphs,” Computer Journal, vol. 47, no. 2, pp. 193–204, 2004. View at Google Scholar · View at Scopus
  6. J. Fiala, T. Kloks, and J. Kratochvíl, “Fixed-parameter complexity of λ-labelings,” Discrete Applied Mathematics, vol. 113, pp. 59–72, 2001. View at Google Scholar
  7. J. Fiala, P. A. Golovach, and J. Kratochvíl, “Distance-constrained labelings of graphs of bounded treewidth,” in Proceedings of the 32nd International Colloquium on Automata, Languages and Programming (ICALP '05), pp. 360–372, 2005.
  8. R. Hammack, W. Imrich, and S. Klavžar, Handbook of Product Graphs, CRC Press, Boca Raton, Fla, USA, 2nd edition, 2011.
  9. N. Kumar, M. Kumar, and R. B. Patel, “Capacity and interference aware link scheduling with channel assignment in wireless mesh networks,” Journal of Network and Computer Applications, vol. 34, no. 1, pp. 30–38, 2011. View at Publisher · View at Google Scholar · View at Scopus
  10. S. Klavžar and A. Vesel, “Computing graph invariants on rotagraphs using dynamic algorithm approach: the case of (2,1)-colorings and independence numbers,” Discrete Applied Mathematics, vol. 129, pp. 449–460, 2003. View at Google Scholar
  11. M. A. Whittlesey, J. P. Georges, and D. W. Mauro, “On the λ-number of Qn and related graphs,” SIAM Journal on Discrete Mathematics, vol. 8, pp. 499–506, 1995. View at Google Scholar
  12. C. Schwarz and D. S. Troxell, “L( 2, 1 )-labelings of Cartesian products of two cycles,” Discrete Applied Mathematics, vol. 154, no. 10, pp. 1522–1540, 2006. View at Publisher · View at Google Scholar · View at Scopus
  13. P. K. Jha, S. Klavžar, and A. Vesel, “L(2, 1)-labeling of direct product of paths and cycles,” Discrete Applied Mathematics, vol. 145, pp. 317–325, 2005. View at Google Scholar
  14. P. K. Jha, “Optimal L(2, 1)-labeling of strong products of cycles,” IEEE Transactions on Circuits and Systems I, vol. 48, no. 4, pp. 498–500, 2001. View at Publisher · View at Google Scholar · View at Scopus
  15. D. Korže and A. Vesel, “L(2,1)-labeling of strong products of cycles,” Information Processing Letters, vol. 94, no. 4, pp. 183–190, 2005. View at Publisher · View at Google Scholar · View at Scopus
  16. J. J. Sylvester, “Mathematical questions with their solutions,” Educational Times, vol. 41, pp. 171–178, 1884. View at Google Scholar
  17. Z. Shao and A. Vesel, “Integer linear programming model and SAT reduction for distance-constrained labelings of graphs: the case of L(3, 2, 1)-labeling for products of paths and cycles,” IET Communications, vol. 7, no. 8, pp. 715–720, 2013. View at Google Scholar
  18. D. A. Wheeler, “MiniSAT User Guide: How to use the MiniSAT SAT Solver,” http://www.dwheeler.com/essays/minisat-user-guide.html.