The L(2, 1)-labeling on <i>β</i>-product of Graphs

Kamesh Kumar

doi:doi:10.11648/j.ijdst.20180402.13

| Peer-Reviewed

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

Kamesh Kumar

Published in International Journal on Data Science and Technology (Volume 4, Issue 2)

Received: 11 May 2018 Accepted: 1 June 2018 Published: 3 July 2018

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

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.

Published in	International Journal on Data Science and Technology (Volume 4, Issue 2)
DOI	10.11648/j.ijdst.20180402.13
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 K_{1, 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).

Cite This Article

Plain Text BibTeX RIS

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://article.sciencepublishinggroup.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

Author Information

Kamesh Kumar

Faculty of Mathematics, College of Pharmacy, Teerthanker Mahaveer University, Moradabad (U.P.), India

Download PDF

Sections

Plain Text BibTeX RIS

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://article.sciencepublishinggroup.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