THE CORDIAL LABELING FOR THE CARTESIAN PRODUCT BETWEEN PATHS AND CYCLES
DOI:
https://doi.org/10.29121/granthaalayah.v8.i3.2020.166Keywords:
Cartesian Product, Cordial, Cycle, Graph, Labeling, PathAbstract [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.
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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
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