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Abstract
Let G = (V, E) be a graph. An L(3,2,1) labeling of G is a function f : V → N ∪ {0} such that for every u, v ∈ V , |f(u) − f(v)| ≥ 3 if d(u, v) = 1, |f(u) − f(v)| ≥ 2 if d(u, v) = 2, and |f(u) − f(v)| ≥ 1 if d(u, v) = 3. Let k ∈ N, a k − L(3, 2, 1) labeling is a labeling L(3,2,1) where all labels are not greater than k. An L(3,2,1) number of G, denoted by λ(3,2,1)(G), is the smallest non-negative integer k such that G has a k − L(3,2,1) labeling. In this paper, we determine λ(3,2,1) of firecracker graphs.
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References
- Chia, M. L., Kuo, D., Liao, H. Y., Yang, C. H., and Yeh, R. K. (2011): L(3,2,1) - Labeling of Simple Graphs. Taiwan J. Math., 15(6), 2439-2457.
- Clipperton, J., Gehrtz, J., Szaniszlo, Z., and Torkornoo, D. (2005): L(3,2,1)-Labeling of Simple Graphs, VERUM, Valparaiso University.
- Gallian, J. A (2011): Dynamic Survey of Graph Labeling. Electronic Journal of Combinatorics, 18. DS6
- Ganesha L.P., (2018): Pelabelan L(3,2,1) pada Beberapa Kelas Graf, Tesis Program Magister, Institut Teknologi Bandung.
- Hale, W.K. (1980): Frequency Assignment: Theory and Applications. Proc. IEEE, 68, 1497-1414
- Liu., J. Z. and Shao, Z. D. (2004): The L(3,2.1) Labeling Problem on Graphs. Mathematica Applicata, 17(4), 596-602
References
Chia, M. L., Kuo, D., Liao, H. Y., Yang, C. H., and Yeh, R. K. (2011): L(3,2,1) - Labeling of Simple Graphs. Taiwan J. Math., 15(6), 2439-2457.
Clipperton, J., Gehrtz, J., Szaniszlo, Z., and Torkornoo, D. (2005): L(3,2,1)-Labeling of Simple Graphs, VERUM, Valparaiso University.
Gallian, J. A (2011): Dynamic Survey of Graph Labeling. Electronic Journal of Combinatorics, 18. DS6
Ganesha L.P., (2018): Pelabelan L(3,2,1) pada Beberapa Kelas Graf, Tesis Program Magister, Institut Teknologi Bandung.
Hale, W.K. (1980): Frequency Assignment: Theory and Applications. Proc. IEEE, 68, 1497-1414
Liu., J. Z. and Shao, Z. D. (2004): The L(3,2.1) Labeling Problem on Graphs. Mathematica Applicata, 17(4), 596-602