RADIO LABELING OF BANANA GRAPHS

  • Sarbaini Sarbaini Department of Mathematics, Faculty of Sciences Technology, Universitas Islam Negeri Sultan Syarif Kasim, Indonesia
  • Nazaruddin Nazaruddin Department of Industrial Engineering, Faculty of Sciences Technology, Universitas Islam Negeri Sultan Syarif Kasim, Indonesia
  • Muhammad Rizki Department of Industrial Engineering, Faculty of Sciences Technology, Universitas Islam Negeri Sultan Syarif Kasim, Indonesia
  • Muhammad Isnaini Hadiyul Umam Department of Industrial Engineering, Faculty of Sciences Technology, Universitas Islam Negeri Sultan Syarif Kasim, Indonesia
  • Muhammad Luthfi Hamzah Department of Information System, Faculty of Sciences Technology, Universitas Islam Negeri Sultan Syarif Kasim, Indonesia
  • Tegar Arifin Prasetyo Institut Teknologi Del, Indonesia
Keywords: banana graphs, graph theory, labeling

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.

Downloads

Download data is not yet available.

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.

Published
2023-04-16
How to Cite
[1]
S. Sarbaini, N. Nazaruddin, M. Rizki, M. Umam, M. Hamzah, and T. Prasetyo, “RADIO LABELING OF BANANA GRAPHS”, BAREKENG: J. Math. & App., vol. 17, no. 1, pp. 0165-0170, Apr. 2023.