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References

[1] W. K. Hale, “Frequency Assignment: Theory and Applications,” Proceedings of IEEE, Vol. 68, No. 12, 1980, pp. 1497-1514. doi:10.1109/PROC.1980.11899

[2] A. A. Bertossi and M. A. Bonuccelli, “Code Assignment for Hidden Terminal Interference Avoidance in Multihope Packet Radio Networks,” IEEE/ACM Transactions on Networking, Vol. 3, No. 4, 1995, pp. 441-449.
doi:10.1109/90.413218

[3] X. T. Jin and R. K. Yeh, “Graph Distance-Dependent Labelling Related to Code Assignment in Computer Networks,” Naval Research Logistics, Vol. 51, 2004, pp. 159-164.

[4] T. Makansi, “Transmitter-Oriented Code Assignment for Multihop Packet Radio,” IEEE Transactions on Communications, Vol. 35, No. 12, 1987, pp. 1379-1382.
doi:10.1109/TCOM.1987.1096728

[5] J. P. Georges and D. W. Mauro, “Generalized Vertex Labeling with a Condition at Distance Two,” Congressus Numerantium, Vol. 140, 1995, pp. 141-159.

[6] A. A. Bertossi, M. C. Pinotti and R. Rizzi, “Channel Assignment on Strongly-Simplicial Graphs,” IEEE Proceedings of International Parallel and Distributed Processing Symposium (IPDPS’03), Nice, 22-26 April 2003, pp. 22-26.

[7] H. L. Bodlaender, T. Kloks, R. B. Tan and J. Van Leeuwen, “Approximations for λ-Colorings of Graphs,” The Computer Journal, Vol. 47, No. 2, 2004, pp. 193-204.
doi:10.1093/comjnl/47.2.193

[8] T. Calamoneri, “The *L*(h, k)-Labelling Problem: A Survey and Annotated Bibliography,” The Computer Journal, Vol. 49, No. 5, 2009, pp. 585-630.
doi:10.1093/comjnl/bxl018

[9] P. J. Wan, “Wear-Optimal Conflict-Free Channel Set Assignments for an Optical Cluster-Based Hypercube Network,” Journal of Combinatorial Optimization, Vol. 1, 1997, pp. 179-186. doi:10.1023/A:1009759916586

[10] N. Alon and B. Mohar, “The Chromatic Number of Graph Powers,” Combinatorics, Probability and Computing, Vol. 11, No. 1, 2002, pp. 1-10.
doi:10.1017/S0963548301004965

[11] S. H. Chiang and J. H. Yan, “On *L*(d, 1)-Labeling of Cartesian Product of a Path,” Discrete Applied Mathematics, Vol. 156, No. 15, 2008, pp. 2867-2881.
doi:10.1016/j.dam.2007.11.019

[12] J. R. Griggs and R. K. Yeh, “Labeling Graphs with a Condition at Distance 2,” SIAM Journal on Discrete Mathematics, Vol. 5, No. 4, 1992, pp. 586-595.
doi:10.1137/0405048

[13] R. K. Yeh, “Labeling Graphs with a Condition at Distance Two,” Ph.D Thesis, University of South Carolina, Columbia, 1990.

[14] D. Kral and R. Skrekovski, “A Theorem on Channel Assignment Problem,” SIAM Journal on Discrete Mathematics, Vol. 16, No. 3, 2003, pp. 426-437.
doi:10.1137/S0895480101399449

[15] D. Goncalves, “On the *L*(p,1)-Labelling of Graphs, in: EuroCom 2005,” Discrete Mathematics and Theoretical Computer Science Proceedings, Vol. AE, 2005, pp. 81-86.

[16] J. Van den Heuvel and S. McGuinnes, “Coloring the Square of a Plannar Graph,” Journal of Graph Theory, Vol. 42, No. 2, 2003, pp. 110-124.
doi:10.1002/jgt.10077

[17] M. Molloy and M. R. Salavatipour, “A Bound on the Chromatic Number of the Square of a Planar Graph,” Journal of Combinatorial Theory, Series B, Vol. 94, No. 2, 2005, pp. 189-213. doi:10.1016/j.jctb.2004.12.005

[18] W. F. Wang and K. W. Lih, “Labelling Planar Graphs with Conditions on Girth and Distance Two,” SIAM Journal on Discrete Mathematics, Vol. 17, 2004, pp. 499-509.

[19] N. Khan, A. Pal and M. Pal, “*L*(2,1)-Labelling of Cactus Graphs,” Communicated.

[20] S. S. Adams, J. Cass, M. Tesch, D. S. Troxell and C. Wheeland, “The Minimum Span of *L*(2,1)-Labeling of Certain Generalized Petersen Graphs,” Discrete Applied Mathematics, Vol. 155, No. 1, 2007, pp. 1314-1325.
doi:10.1016/j.dam.2006.12.001

[21] G. J. Chang, W. T. Ke, D. Kuo, D. D. F. Lin and R. K. Yeh, “On *L*(d,1)-Labellings of Graphs,” Discrete Mathematics, Vol. 220, 2000, pp. 57-66.
doi:10.1016/S0012-365X(99)00400-8

[22] G. J. Chang and C. Lu, “Distance Two Labelling of Graphs,” European Journal of Combinatorics, Vol. 24, 2003, pp. 53-58. doi:10.1016/S0195-6698(02)00134-8

[23] J. Fiala, T. Kloks and J. Kratochvil, “Fixed-Parameter Complexity of λ-Labelling,” Discrete Applied Mathematics, Vol. 133, No. 1, 2001, pp. 59-72.
doi:10.1016/S0166-218X(00)00387-5

[24] J. Georges and D. W. Mauro, “On Generalized Petersen Graphs Labelled with a Condition at Distance Two,” Discrete Mathematics, Vol. 259, No. 1-3, 2002, pp. 311-318. doi:10.1016/S0012-365X(02)00302-3

[25] J. Georges, D. W. Mauro and M. I. Stein, “Labelling Products of Complete Graphs with a Condition at Distance Two,” SIAM Journal on Discrete Mathematics, Vol. 14, 2000, pp. 28-35. doi:10.1137/S0895480199351859

[26] P. K. Jha, “Optimal *L*(2,1)-Labelling of Cartesian Products of Cycles with an Application to Independent Domination,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, Vol. 47, No. 10, 2000, pp. 1531-1534. doi:10.1109/81.886984

[27] S. Klavzar and A. Vesel, “Computing Graph Invariants on Rotagraphs Using Dynamic Algorithm Approach: The Case of *L*(2,1)-Colorings and Independence Numbers,” Discrete Applied Mathematics, Vol. 129, 2003, pp. 449-460. doi:10.1016/S0166-218X(02)00597-8

[28] D. Kuo and J. H. Yan, “On *L*(2,1)-Labelling of Cartesian Products of Paths and Cycles,” Discrete Mathematics, Vol. 283, No. 1-3, 2004, pp. 137-144.
doi:10.1016/j.disc.2003.11.009

[29] C. Schwarz and D. S. Troxell, “*L*(2,1)-Labelling of Products of Two Cycles,” Discrete Applied Mathematics, Vol. 154, No. 1-3, 2006, pp. 1522-1540.
doi:10.1016/j.dam.2005.12.006

[30] R. K. Yeh, “The Edge Span of Distance Two Labelling of Graphs,” Taiwanese Journal of Mathematics, Vol. 4, No. 4, 2000, pp. 675-683.

[31] R. Battiti, A. A. Bertossi and M. A. Bonuccelli, “Assigning Code in Wireless Networks: Bounds and Scaling Properties,” Wireless Networks, Vol. 5, No. 3, 1999, pp. 195-209. doi:10.1023/A:1019146910724