The L (2, 1)-labeling of K1, n-free graphs and its applications

Applied Mathematics Letters

Volumn 21, Issue 11, 2008, Pages 1188-1193

  Shao, Zhendong ^a   Yeh, Roger K ^b   Poon, Kin Keung ^c   Shiu, Wai Chee ^d  

^a UNIVERSITY OF WESTERN ONTARIO   (Canada)

^b FENG CHIA UNIVERSITY   (Taiwan)

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

^d HONG KONG BAPTIST UNIVERSITY   (Hong Kong)

Author keywords

Channel assignment; K1, n free simple graph; L (2, 1) labeling; Unit sphere graph

Indexed keywords

CHANNEL ASSIGNMENT; K1, N-FREE SIMPLE GRAPH; L (2, 1)-LABELING; UNIT SPHERE GRAPH;

LABELING;

LABELING; MATHEMATICAL ANALYSIS; PROBLEM SOLVING;

EID: 51049121343     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aml.2007.12.020     Document Type: Article

References (22)

1. Bodlaender H.L., Kloks T., Tan R.B., and von Leeuwen J. λ-coloring of graphs. Lecture Notes in Computer Science vol. 1770 (2000), Springer-Verlag, Berlin, Heidelberg 395-406
2. Chang G.J., Ke W.-T., Kuo D., Liu D.D.-F., and Yeh R.K. On L (d, 1)-labelings of graphs. Discrete Math. 220 (2000) 57-66
3. Chang G.J., and Kuo D. The L (2, 1)-labeling on graphs. SIAM J. Discrete Math. 9 (1996) 309-316
4. Conway J.H., and Sloane N.J.A. Sphere Packing, Lattices, and Groups. 2nd ed. (1993), Springer-Verlag, New York
5. Fiala J., Kloks T., and Kratochvíl J. Fixed-parameter complex of λ-labelings. Lecture Notes in Computer Science vol. 1665 (1999), Springer-Verlag, Berlin, Heidelberg 350-363
6. Georges J., and Mauro D.W. On the criticality of graphs labelled with a condition at distance two. Congr. Numer. 101 (1994) 33-49
7. Georges J., and Mauro D.W. On the size of graphs labeled with a condition at distance two. J. Graph Theory 22 (1996) 47-57
8. Georges J., and Mauro D.W. Edge Labelings with a condition at distance two. Ars Combin. 70 (2004) 109-128
9. Griggs J.R., and Yeh R.K. Labeling graphs with a condition at distance two. SIAM J. Discrete Math. 5 (1992) 586-595
10. Hale W.K. Frequency assignment: Theory and applications. Proc. IEEE 68 (1980) 1497-1514
11. Harary F. Graph Theory (1969), Addison-Wesley, Reading, MA
12. Jha P.K., Narayanan A., Sood P., Sundaram K., and Sunder V. On L (2, 1)-labeling of the Cartesian product of a cycle and a path. Ars Combin. 55 (2000) 81-89
13. Král' D., and S ̌krekovski R. A theorem about channel assignment problem. SIAM J. Discrete Math. 16 3 (2003) 426-437
14. Kuo D., and Yan J.-H. On L(2, 1)-labeling of Cartesian products of paths and cycles. Discrete Math. 283 1-3 (2004) 137-144
15. Liu D.D.-F., and Yeh R.K. On distance-two labelings of graphs. Ars Combin. 47 (1997) 13-22
16. Roberts F.S. T-colorings of graphs: Recent results and open problems. Discrete Math. 93 (1991) 229-245
17. Sakai D. Labeling chordal graphs with a condition at distance two. SIAM J. Discrete Math. 7 (1994) 133-140
18. Z. Shao, S. Klavžar, W.C. Shiu, D. Zhang, Improved bounds on the L (2, 1)-number of direct and strong products of graphs, IEEE Trans. Circuits and Systems II: Express Briefs (in press)
19. Shao Z., and Yeh R.K. The L (2, 1)-labeling and operations of graphs. IEEE Trans. Circuits Syst. I: Regular Papers 52 (2005) 668-671
20. N.J.A. Sloane, G. Nebe, Table of highest kissing numbers presently known. http://www.research.att.com/~njas/lattices/kiss.html
21. R.K. Yeh, Labeling graphs with a condition at distance two, Ph.D. thesis, Dept. of Math., Univ. of South Carolina, 1990
22. Yeh R.K. The edge span of distance two labelings of graphs. Taiwanese J. Math. 4 (2000) 675-683