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Volume 7, Issue 4, August 2018, Page: 203-211
The Cordial Labeling for the Four-Leaved Rose Graph
Ashraf Elrokh, Department of Math, Faculty of Science, Menoufia University, Shebeen Elkom, Egypt
Received: Jun. 22, 2018;       Accepted: Aug. 31, 2018;       Published: Oct. 15, 2018
Abstract
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
Keywords
Cactus Graph, Cordial Labeling, Four-Leaved Rose Graph
Ashraf Elrokh, The Cordial Labeling for the Four-Leaved Rose Graph, Applied and Computational Mathematics. Vol. 7, No. 4, 2018, pp. 203-211. doi: 10.11648/j.acm.20180704.14
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