A new approach to the L(2, 1)-labeling of some products of graphs

IEEE Transactions on Circuits and Systems II: Express Briefs

Volumn 55, Issue 8, 2008, Pages 802-805

  Shiu, Wai Chee ^a   Shao, Zhendong ^b   Poon, Kin Keung ^c   Zhang, David ^d  

^a HONG KONG BAPTIST UNIVERSITY   (Hong Kong)

^b UNIVERSITY OF WESTERN ONTARIO   (Canada)

^c THE EDUCATION UNIVERSITY OF HONG KONG   (Hong Kong)

^d HONG KONG POLYTECHNIC UNIVERSITY   (Hong Kong)

Author keywords

Cartesian product; Channel assignment; Direct product; L(2,1) labeling; Lexicographic product; Strong product

Indexed keywords

COMBINATORIAL OPTIMIZATION; FREQUENCY ALLOCATION; RADIO TRANSMISSION; TRANSMITTERS;

CARTESIAN PRODUCTS; CHANNEL ASSIGNMENT; DIRECT PRODUCT; L(2 , 1)-LABELING; LEXICOGRAPHIC PRODUCT; STRONG PRODUCT;

GRAPH THEORY;

FREQUENCY; LABELING; MATRICES; SEPARATION; STANDARDS; TRANSMITTERS;

EID: 50549094453     PISSN: 15497747     EISSN: 15583791     Source Type: Journal    
DOI: 10.1109/TCSII.2008.922450     Document Type: Article

References (23)

1. S. S. Adams, J. Cass, and D. S. Troxell, "An extension of the channel-assignment problem: L(2, 1)-labelings of generalized Petersen graphs," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 53, no. 6, pp. 1101-1107, Jun. 2006.
2. H. L. Bodlaender, T. Kloks, R. B. Tan, and J. V. Leeuwen, "λ-coloring of graphs," in Lecture Notes in Computer Science. Berlin, Germany: Springer-Verlag, 2000, vol. 1770, pp. 395-406.
3. T. Calamoneri, "The L(h. k)-labelling problem: A survey and snnotated bibliography," Comp. J., vol. 49, pp. 585-608, 2006.
4. G. J. Chang and D. Kuo, "The L(2, 1)-labeling on graphs," SIAM J. Discr. Math., vol. 9, pp. 309-316, 1996.
5. D. M. Cvetković, M. Doob, and H. Sachs, Spectra of Graphs - Theory and Application, 2nd ed. New York: Academic, 1982.
6. J. Fiala, T. Kloks, and J. Kratochvíl, "Fixed-parameter complex of λ-labelings," in Lecture Notes in Computer Science. Berlin, Germany: Springer-Verlag, 1999, vol. 1665, pp. 350-363.
7. N. Funabiki and Y. Takefuji, "A neural network parallel algorithm for channel assignment problem in cellular radio networks," IEEE Trans. Veh. Technol., vol. 41, no. 4, pp. 430-437, Apr. 1992.
8. J. R. Griggs and R. K. Yeh, "Labeling graphs with a condition at distance two," SIAM J. Discr. Math., vol. 5, pp. 586-595, 1992.
9. W. K. Hale, "Frequency assignment: Theory and application," Proc. IEEE, vol. 68, pp. 1497-1514, 1980.
10. W. Imrich and S. Klavžar, Product Graphs: Structure and Recognition. New York: Wiley, 2000.
11. P. K. Jha, "Optimal L(2, 1)-labelings of Cartesian products of cycles with an application to independent domination," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 47, no. 12, pp. 1531-1534, Dec. 2000.
12. P. K. Jha, "Optimal L(2, 1)-labeling of strong product cycles," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 48, no. 4, pp. 498-500, Apr. 2001.
13. 2-conjecture for L(2,1)-labelings is true for direct and strong products of graphs," IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 53, no. 4, pp. 274-277, Mar. 2006.
14. N. Kunz, "Channel assignment for cellular radio using neural networks," IEEE Trans. Veh. Technol., vol. 40, pp. 188-193, 1992.
15. D. Korže and A. Vesel, "L(2, 1)-labeling of strong products of cycles," Inf. Proc. Lett., vol. 94, pp. 183-190, 2005.
16. D. Král and R. Škrekovski, "A theorem about channel assignment problem," SIAM J. Discr. Math., vol. 16, pp. 426-437, 2003.
17. W. K. Lai and G. G. Coghill, "Channel assignment through evolutionary optimization," IEEE Trans. Veh. Technol., vol. 45, no. 1, pp. 91-96, Jan. 1996.
18. R. Mathar, "Channel assignment in cellular radio networks," IEEE Trans. Veh. Technol., vol. 42, no. 6, pp. 647-656, Jun. 1993.
19. F. S. Roberts, "T-colorings of graphs: Recent results and open problems," Discr. Math., vol. 93, pp. 229-245, 1991.
20. Z. Shao, S. Klavžar, W. C. Shiu, and D. Zhang, "Improved bounds on the L(2, 1)-number of direct and strong products of graphs," IEEE Trans. Circuits Syst. II, Exp. Briefs, to be published.
21. Z. Shao and R. K. Yeh, "The L(2, 1)-labeling and operations of graphs," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 52, no. 4, pp. 668-671, Apr. 2005.
22. K. W. Tang and S. A. Padubirdi, "Diagonal and toroidal mesh networks," IEEE Trans. Comput., vol. 43, no. 8, pp. 815-826, Aug. 1994.
23. 7," Inf. Proc. Lett., vol. 81, pp. 277-282, 2002.