International Journal on Data Science and Technology

| Peer-Reviewed |

The L(2, 1)-labeling on β-product of Graphs

Received: 11 May 2018    Accepted: 01 June 2018    Published: 03 July 2018
Views:       Downloads:

Share This Article

Abstract

The L(2, 1)-labeling (or distance two labeling) of a graph G is an integer labeling of G in which two vertices at distance one from each other must have labels differing by at least 2 and those vertices at distance two must differ by at least 1. The L(2, 1)-labeling number of G is the smallest number k such that G has an L(2, 1)-labeling with maximum of f(v) is equal to k, where v belongs to vertex set of G. In this paper, upper bound for the L(2, 1)-labeling number for the β-product of two graphs has been obtained in terms of the maximum degrees of the graphs involved.

DOI 10.11648/j.ijdst.20180402.13
Published in International Journal on Data Science and Technology (Volume 4, Issue 2, June 2018)
Page(s) 54-59
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Channel Assignment, L(2, 1)-labeling, L(2, 1)-labeling Number, Graph β-product

References
[1] Chang G. J. and D. Kuo D., The L(2, 1)-labeling on graphs, SIAM J. Discrete Math., Vol. 9, 309-316 (1996).
[2] Chang G. J., Ke W. T., Kuo D., Liu D. D. F. and Yeh R. K., On L(d, 1)-labeling of graphs, Discrete Math, Vol. 220, 57-66 (2000).
[3] El-Kholy E. M., Lashin E. S., and Daoud S. N., New operations on graphs and graph foldings, International Mathematical Forum, Vol. 7, 2253-2268(2012).
[4] Gonccalves D., On the L(p, 1)-labeling of graphs, in Proc. 2005 Eur. Conf. Combinatorics, Graph Theory Appl. S. Felsner, Ed., 81-86(2005).
[5] Griggs J. R. and Yeh R. K., Labeling graphs with a condition at distance two, SIAM J. Discrete Math., Vol. 5, 586-595(1992).
[6] Hale W. K., Frequency assignment: Theory and application, Proc. IEEE, Vol. 68, No. 6, 1497-1514(1980).
[7] Jha P. K., Optimal L(2, 1)-labeling of strong product of cycles, IEEE Trans. Circuits systems-I, Fundam. Theory Appl., Vol. 48, No. 4, 498-500(2001).
[8] Jha P. K., Optimal L(2, 1)-labeling on Cartesian products of cycles with an application to independent domination, IEEE Trans. Circuits systems-I, Fundam. Theory Appl., Vol. 47, No. 121531-1534, (2000).
[9] Klavzar S. and Spacepan S., The △2 -conjecture for L(2, 1)-labelings is true for direct and strong products of graphs, IEEE Trans. Circuits systems-II, Exp. Briefs, Vol. 53, No. 3, 274-277(2006).
[10] Kral D. and Skrekovski R., A theorem about channel assignment problem, SIAM J. Discrete Math., 16, 426-437(2003).
[11] Liu D. D. F. and Yeh R. K., On Distance Two Labeling of Graphs, Ars combinatoria, Vol. 47, 13-22(1997).
[12] Pradhan P. and Kumar K., The L(2, 1)-labeling of α-product of graphs, Annals of Pure and Applied Mathematics, Vol. 10, No. 1, 29-39(2015).
[13] Roberts F. S., T-colorings of graphs: Recent results and open problems, Discrete Math., Vol. 93, 229-245(1991).
[14] Sakai D., Labeling Chordal Graphs with a condition at distance two, SIAM J. Discrete Math., Vol. 7, 133-140(1994).
[15] Shao Z., Klavzar S., Shiu W. C. and Zhang D., Improved bounds on the L(2, 1)-number of direct and strong products of graphs, IEEE Trans. Circuits systems-II, Exp. Briefs, Vol. 55, No. 7, 685-689(2008).
[16] Shao Z. and Yeh R. K., The L(2, 1)-labeling and operations of graphs, IEEE Trans. Circuits and Systems-I: Regul. Paper, Vol. 52, No. 4, 668-671(2005).
[17] Shao Z. and Zhang D., The L(2, 1)-labeling on Cartesian sum of graphs, Applied Mathematics Letters, Vol. 21, 843-848(2008).
[18] Shao Z., Yeh R. K., Poon K. K. and Shiu W. C., The L(2, 1)-labeling of K1, n-free graphs and its applications, Applied Mathematics Letters, Vol. 21, 1188-1193(2008).
[19] Shao Z., Yeh R. K. and Zhang D., The L(2, 1)-labeling on graphs and the frequency assignment problem, Applied Mathematics Letters, Vol. 21, 37-41(2008).
[20] Vaidya S. K. and Bantva D. D., Distance two labeling of some total graphs, Gen. Math. Notes, Vol. 3, No. 1, 100-107(2011).
[21] Vaidya S. K. and Bantva D. D., Some new perspectives on distance two labeling, International Journal of Mathematics and Soft Computing Vol. 3, No. 3, 7-13(2013).
[22] Lin W. S. and Dai B., On (s, t)-relexed L(2, 1)-labeling of the triangular lattic, Journal of Combinatorial Optimization, Vol. 29, No. 3, 655-669(2015).
[23] Lin W. S., On (s, t)-relexed L(2, 1)-labeling of graphs, Journal of Combinatorial Optimization, Vol. 31, No. 1, 405-426(2016).
[24] Lafon M. B., Chen S., Karst M., OelirlienJ. And Troxell D. S., Labeling crossed prisms with a condition at distance two, Involve a Journal of Mathematics, Vol. 11, No. 1, 67-80(2018).
Author Information
  • Faculty of Mathematics, College of Pharmacy, Teerthanker Mahaveer University, Moradabad (U.P.), India

Cite This Article
  • APA Style

    Kamesh Kumar. (2018). The L(2, 1)-labeling on β-product of Graphs. International Journal on Data Science and Technology, 4(2), 54-59. https://doi.org/10.11648/j.ijdst.20180402.13

    Copy | Download

    ACS Style

    Kamesh Kumar. The L(2, 1)-labeling on β-product of Graphs. Int. J. Data Sci. Technol. 2018, 4(2), 54-59. doi: 10.11648/j.ijdst.20180402.13

    Copy | Download

    AMA Style

    Kamesh Kumar. The L(2, 1)-labeling on β-product of Graphs. Int J Data Sci Technol. 2018;4(2):54-59. doi: 10.11648/j.ijdst.20180402.13

    Copy | Download

  • @article{10.11648/j.ijdst.20180402.13,
      author = {Kamesh Kumar},
      title = {The L(2, 1)-labeling on β-product of Graphs},
      journal = {International Journal on Data Science and Technology},
      volume = {4},
      number = {2},
      pages = {54-59},
      doi = {10.11648/j.ijdst.20180402.13},
      url = {https://doi.org/10.11648/j.ijdst.20180402.13},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ijdst.20180402.13},
      abstract = {The L(2, 1)-labeling (or distance two labeling) of a graph G is an integer labeling of G in which two vertices at distance one from each other must have labels differing by at least 2 and those vertices at distance two must differ by at least 1. The L(2, 1)-labeling number of G is the smallest number k such that G has an L(2, 1)-labeling with maximum of f(v) is equal to k, where v belongs to vertex set of G. In this paper, upper bound for the L(2, 1)-labeling number for the β-product of two graphs has been obtained in terms of the maximum degrees of the graphs involved.},
     year = {2018}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - The L(2, 1)-labeling on β-product of Graphs
    AU  - Kamesh Kumar
    Y1  - 2018/07/03
    PY  - 2018
    N1  - https://doi.org/10.11648/j.ijdst.20180402.13
    DO  - 10.11648/j.ijdst.20180402.13
    T2  - International Journal on Data Science and Technology
    JF  - International Journal on Data Science and Technology
    JO  - International Journal on Data Science and Technology
    SP  - 54
    EP  - 59
    PB  - Science Publishing Group
    SN  - 2472-2235
    UR  - https://doi.org/10.11648/j.ijdst.20180402.13
    AB  - The L(2, 1)-labeling (or distance two labeling) of a graph G is an integer labeling of G in which two vertices at distance one from each other must have labels differing by at least 2 and those vertices at distance two must differ by at least 1. The L(2, 1)-labeling number of G is the smallest number k such that G has an L(2, 1)-labeling with maximum of f(v) is equal to k, where v belongs to vertex set of G. In this paper, upper bound for the L(2, 1)-labeling number for the β-product of two graphs has been obtained in terms of the maximum degrees of the graphs involved.
    VL  - 4
    IS  - 2
    ER  - 

    Copy | Download

  • Sections