The Cordiality of the Join and Union of the Second Power of Fans
Applied and Computational Mathematics
Volume 7, Issue 6, December 2018, Pages: 219-224
Received: Dec. 9, 2018;
Accepted: Jan. 5, 2019;
Published: Jan. 28, 2019
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Shokry Nada, Department of Math, Faculty of Science, Menoyfia University, Shebeen Elkom, Egypt
Ashraf Elrokh, Department of Math, Faculty of Science, Menoyfia University, Shebeen Elkom, Egypt
Eman Elshafey, Department of Math, Faculty of Science, El- Azhar University, Cairo, Egypt
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A graph is called cordial if it has a 0-1 labeling that satisfies certain conditions. A second power of a fan Fn 2 is the join of the null graph N1 and the second power of path Pn2, i.e. Fn2 = N1 + Pn2. In this paper, we study the cordiality of the join and union of pairs of the second power of fans. and give the necessary and sufficient conditions that the join of two second powers of fans is cordial. we extend these results to investigate the cordiality of the join and the union of pairs of the second power of fans. Similar study is given for the union of such second power of fans. AMS Classification: 05C78.
Join Graph, Second Power Graph, Cordial Graph
To cite this article
The Cordiality of the Join and Union of the Second Power of Fans, Applied and Computational Mathematics.
Vol. 7, No. 6,
2018, pp. 219-224.
Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cahit, On cordial and 3-equitable labelings of graphs, Utilities Math., 37 (1990).
A. T. Diab, and E. A. Elsakhaw,. Some Results on Cordial Graphs, Proc. Math. Phys. Soc. Egypt, No.7, pp. 67-87 (2002).
A. T. Diab,Study of Some Problems of Cordial Graphs, Ars Combinatoria 92 (2009), pp. 255-261.
A. T. Diab, On Cordial Labelings of the Second Power of Paths with Other Graphs, Ars Combinatoria 97A(2010), pp. 327-343.
J. A.Gallian, A dynamic survey of graph labeling, The Electronic Journal of Combinatorics, (December 29, 2014).
S. W. Golomb, How to number a graph in Graph Theory and Computing, R.C. Read, ed., Academic Press, New York (1972) 23-37.
R. L. Graham and N. J. A.Sloane, On additive bases and harmonious graphs, SIAM J. Alg. Discrete Math.,1(1980) 382404.
Rosa, On certain valuations of the vertices of a graph, Theory of Graphs (Internet. Symposium, Rome, July 1966), Gordon and Breach, N. Y. and Dunod Paris (1967) 349-355.