L(2,1)-Labeling Number of the Product and the Join Graph on Two Fans

Sumei Zhang, Qiaoling Ma

School of Mathematical Sciences, University of Jinan, Jinan, China.

DOI: 10.4236/am.2013.47147                

Abstract

L(2,1)-labeling number of the product and the join graph on two fans are discussed in this paper, we proved that L(2,1)-labeling number of the product graph on two fans is λ(G) ≤ Δ+3 , L(2,1)-labeling number of the join graph on two fans is λ(G) ≤ 2Δ+3.

Keywords

Labeling Number; Join Graph; Product Graph

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	J. A. Bondy and U. S. R. Murty, “Graph Theory with Applications,” Macmillan, New York, 1976.
[2]	W. K. Hale, “Frequency Assignment: Theory and Appli cations,” IEEE Proceedings, Vol. 68, No. 12, 1980, pp. 1497-1514. doi:10.1109/PROC.1980.11899
[3]	J. R. Griggs and R. K. Yeh, “Labeling Graphs with a Condition at Distance 2,” SIAM Journal on Discrete Ma thematics, Vol. 5, No. 4, 1992, pp. 586-595. doi:10.1137/0405048
[4]	G. J. Chang and D. Kuo, “The L(2,1)-Labeling Problem on Graphs,” SIAM Journal on Discrete Mathematics, Vol. 9, No. 2, 1996, pp. 309-316. doi:10.1137/S0895480193245339
[5]	D. Král and R. A. skrekovski, “Theorem about the Chan nel Asscgnment Problem,” SIAM Journal on Discrete Mathematics, Vol. 16, No. 3, 2003, pp. 426-437. doi:10.1137/S0895480101399449
[6]	J. P. Georges, D. W. Mauro and M. I. Stein, “Labeling Products of Complete Graphs with a Condition at Dis tance Two,” SIAM Journal on Discrete Mathematics, Vol. 14, No. 1, 2000, pp. 28-35. doi:10.1137/S0895480199351859
[7]	J. P. Georges, D. W. Mauro and M. A. Whittlesey, “Re lating Path Covering to Vertex Labelling with a Condi tion at Distance Two,” Discrete Mathematics, Vol. 135, 1994, pp. 103-111. doi:10.1016/0012-365X(93)E0098-O
[8]	S. M. Zhang and Q. L. Ma, “On List (2,1)-Labelling of Some Planar Graphs,” Ars Combinatoria, Vol. 84, 2007, pp. 231-241.
[9]	S. M. Zhang and Q. L. Ma, “Labelling Some Planar Graphs with a Condition at Distance Two,” Journal of Applied Mathematics and Computing, Vol. 24, No. 1-2, 2007, pp. 421-426.
[10]	S. M. Zhang and J. H. Wang, “L(p,q)-Labeling of Planar Graph with High Maximum Degree,” Journal of Shan dong University, Vol. 42, No. 4, 2007, pp. 39-43.
[11]	S. M. Zhang and Q. L. Ma, “L(d,1)-Total Labeling of Ou terplannar Graphs,” Journal of Jinnan University, Vol. 20, No. 3, 2006, pp. 258-260.