The Cordial Labeling for the Four-Leaved Rose Graph
Applied and Computational Mathematics
Volume 7, Issue 4, August 2018, Pages: 203-211
Received: Jun. 22, 2018;
Accepted: Aug. 31, 2018;
Published: Oct. 15, 2018
Views 691 Downloads 65
Ashraf Elrokh, Department of Math, Faculty of Science, Menoufia University, Shebeen Elkom, Egypt
Follow on us
A cactus graph with four blocks which are all cycles, not necessarily be of the same size, is called four-leaved rose graph and denoted by Ln, m, k, s, where n, m, k and s represent she sizes of the four cycles. A cordial graph is a graph whose vertices and edges have 0-1 labeling in such a way that the number of vertices (edges) labelled with zeros and the number of vertices (edges) labelled with ones differ absolutely by at most one .In this paper, we study this graph in detail and show that any four-leaved rose graph is cordial for all n, m, k and s except possibly at n, m are odd with (k + s) = 0(mod4) or n, m are even with (k + s) = 2(mod4). Our technique depends on the methods that partition off the set of positive integers and then use suitable labeling in each division of the partition to achieve our results. AMS classification 05C76, 05C78
Cactus Graph, Cordial Labeling, Four-Leaved Rose Graph
To cite this article
The Cordial Labeling for the Four-Leaved Rose Graph, Applied and Computational Mathematics.
Vol. 7, No. 4,
2018, pp. 203-211.
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.
Rosa, A. , On certain valuations of the vertices of a graph, Theory of Graphs( Internat Symposium, Rome, July 1966),Gordon and Breach, N.Y.and Dunod Paris, (1967) 349- 355.
Graham, R. L. and Sloane, N.J.A., On additive bases and harmonious graphs, SIAM J. Alg. Discrete Math. 1, (1980) 382-404.
Elrokh, A. and Atef Mohamed, The cordiality of lemniscate graph and its second power, Malaysian journal of mathematical science , 2017 under review
Elrokh, A., The cordiality of the three-leaved rose graph, submitted 2018.
Diab, A. T. , On Cordial Labelings of Wheels with Other Graphs, ARS Combinatoria 100, (2011) 265-279.
Golomb, S. W., How to number a graph in Graph Theory and Computing,R.C. Read, ed., Academic Press, New York, (1972) 23-37.
Gallian, J. A. , A dynamic survey of graph labeling, The Electronic Journal of Combina- torics 17, December 29 (2014).
Cahit, I. , Cordial Graphs: A Weaker Version of Graceful and Harmonious Graphs, Ars Combin. 23(1987) 201-207.
Kirchherr, W. W., On the cordiality of some specific graphs, ARS Combinatoria 31(1991), pp 127-138.
Lee, S. M. and Liu, A. , A construction of cordial graphs from smaller cordial graphs, Ars Combin., 32(1991) 209-214.