RADIO LABELING OF BANANA GRAPHS
Abstract
Let G=(V, E) be a graph. An L(3,2,1) labeling of G is a function such that for every , , and if . Let , a labeling is a labeling where all labels are not greater than . An ) number of , denoted by , is the smallest non-negative integer such that has a labeling. In this paper, we determine of banana graphs.
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References
W. K. Hale, “Frequency assignment: Theory and applications,” Proc. IEEE, vol. 68, no. 12, pp. 1497–1514, 1980.
F. S. Roberts, “T-colorings of graphs: recent results and open problems,” Discrete Math., vol. 93, no. 2–3, pp. 229–245, 1991.
A. A. Bertossi and C. M. Pinotti, “Approximate L (δ1, δ2,…, δt)‐coloring of trees and interval graphs,” Networks An Int. J., vol. 49, no. 3, pp. 204–216, 2007.
D. Indriati and T. S. M. N. Herlinawati, “L (d, 2, 1)-labeling of star and sun graphs,” Math. Theory Model., vol. 4, no. 11, 2012.
N. Khan, M. Pal, and A. Pal, “L (0, 1)-labeling of cactus graphs,” 2012.
B. M. Kim, W. Hwang, and B. C. Song, “$L(3,2,1)$-Labeling For The Product Of A Complete Graph And A Cycle,” Taiwan. J. Math., vol. 19, no. 3, May 2015, doi: 10.11650/tjm.19.2015.4632.
T. Calamoneri, “The L(h, k)-Labelling Problem: An Updated Survey and Annotated Bibliography,” Comput. J., vol. 54, no. 8, pp. 1344–1371, Aug. 2011, doi: 10.1093/comjnl/bxr037.
S. Ghosh, P. Podge, N. C. Debnath, and A. Pal, “Efficient Algorithm For L (3, 2, 1)-Labeling of Cartesian Product Between Some Graphs,” in Proceedings of 32nd International Conference on, 2019, vol. 63, pp. 111–120.
J. A. Gallian, “A dynamic survey of graph labeling,” Electron. J. Comb., vol. 1, no. DynamicSurveys, p. DS6, 2018.
J. Clipperton, “L (d, 2, 1)-labeling of simple graphs,” Rose-Hulman Undergrad. Math. J., vol. 9, no. 2, p. 2, 2008.
S. Amanathulla and M. Pal, “L (3, 2, 1)-and L (4, 3, 2, 1)-labeling problems on interval graphs,” AKCE Int. J. Graphs Comb., vol. 14, no. 3, pp. 205–215, 2017.
S. Amanathulla, B. Bera, and M. Pal, “L(2,1,1)-Labeling of Circular-Arc Graphs,” J. Sci. Res., vol. 13, no. 2, pp. 537–544, May 2021, doi: 10.3329/JSR.v13i2.50483.
Kusbudiono, I. A. Umam, I. Halikin, and M. Fatekurohman, “L (2,1) Labeling of Lollipop and Pendulum Graphs,” 2022, doi: 10.2991/case.k.220202.010.
M.-L. Chia, D. Kuo, H. Liao, C.-H. Yang, and R. K. Yeh, “$ L (3, 2, 1) $-Labeling Of Graphs,” Taiwan. J. Math., vol. 15, no. 6, pp. 2439–2457, 2011.
M. Chia, D. Kuo, H. Liao, C. Yang, and R. K. Yeh, “L (3 , 2 , 1)-labeling of graphs,” vol. 15, no. 6, pp. 2439–2457, 2011.
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