THE CORDIAL LABELING FOR THE CARTESIAN PRODUCT BETWEEN PATHS AND CYCLES

Authors

  • Mohammed M. Ali Al-Shamiri Department of Mathematics, Faculty of Science and Arts, Mahayil Asir, King Khalid University, K.S.A.
  • A. Elrokh Department of Mathematics, Faculty of Science, Menoufia University, Shebeen Elkom, Egypt
  • Yasser El –Mashtawye Department of Mathematics, Faculty of Science and Arts, Mahayil Asir, King Khalid University, K.S.A.
  • S. Euat Tallah Department of Mathematics, Faculty of Science, Menoufia University, Shebeen Elkom, Egypt

DOI:

https://doi.org/10.29121/granthaalayah.v8.i3.2020.166

Keywords:

Cartesian Product, Cordial, Cycle, Graph, Labeling, Path

Abstract [English]

A graph is said to be cordial if it has a 0-1 labeling that satisfies certain properties. In this paper we show the Cartesian product of a path and a cycle or vice versa are always cordial under some conditions. Also, we prove that the Cartesian product of two paths is cordial.

Downloads

Download data is not yet available.

References

I.Cahit, On cordial and 3-equitable labeling of graphs,Utilities Math.,37(1990).

A. T. Diab, Study of some problems of cordial graphs, ARS Combinatoria. 2009; 92:255-261.

A.T.Diab, On Cordial Labeling of the second power of paths with other graphs , ARS Combinatoria 2010; 97A:327-343.

A. T.Diab, Generalization of some results on cordial graphs , ARS Combinatoria. 2009; 92:161-173.

A.T.Diab,On Cordial Labeling of Wheels with other graphs ,ARS Combinatoria 2011;100:265-279.

J.A.Gallian,A dynamic survey of graph labeling,The electronic Journal of Combinatorics 17,November 2010:13 DS6.

S. W.Golomb, How to number a graph in graph theory and Computing, R.C. Read,rd., Academic Press,New York. 1972: 23-37. DOI: https://doi.org/10.1016/B978-1-4832-3187-7.50008-8

R.L.Graham and N.J.A.Sloane,On additive bases and harmonious graphs, SIAM J. Alg. Discrete Math.1. 1980:382-404. DOI: https://doi.org/10.1137/0601045

A.Rosa,On certain valuations of the vertices of a graph,Theorey of graphs (Internet Symposium , Rome,July 1966),Gordon and Breach,N.Y. and Dunod Paris. 1967:349-355.

M.A Seoud and Abdel Maqusoud, On Cordial and balanced labeling af graphs,J. Egypt. Math. Soc.1999; 7:127-135.

Mohammed M. Ali Al-Shamiri, Shokry I. N, A. I. Elrokh, Yasser Elmshtaye, Some Results on Cordial Digraphs, Open Journal of Discrete Mathematics,2020;10;1:4-12. DOI: https://doi.org/10.4236/ojdm.2020.101002

F. Harary and G.W.Wilcox, Boolean operations on graphs ,Math.Scand. 1967; 20: 41-51 DOI: https://doi.org/10.7146/math.scand.a-10817

Downloads

Published

2020-03-31

How to Cite

Ali Al-Shamiri, M. M., Elrokh, A., El –Mashtawye, Y., & Tallah, S. E. (2020). THE CORDIAL LABELING FOR THE CARTESIAN PRODUCT BETWEEN PATHS AND CYCLES. International Journal of Research -GRANTHAALAYAH, 8(3), 331–341. https://doi.org/10.29121/granthaalayah.v8.i3.2020.166