magic Labelings of Union of Disjoint Complete Multipartite Graphs
Abstract
An magic labeling of a graph is a one to one map from the vertex set to a set of positive integers with , such that for any where is a constant and is the set of vertices in adjacent to . A graph is magic if admits an magic labeling. In this paper, we show a necessary and sufficient condition for the existence of an magic labelings of a union of disjoint complete multipartite graphs , we also prove that the graph adding one edge is not magic if two endpoints of are from the same partite set.Keywords : S-magic ; graph labeling ; multipartite graphReferences
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Gallian, J. A. (2017). A dynamic survey of graph labeling. Electronic Journal of Combinatorics, 20 #Ds6.
Godinho, A. and Singh, T. (2015). On S-magic graphs, Electronic Notes in Discrete Mathematics, 48, 267–273.
Miller, M., Rodger, C. and Simanjuntak, R. (2003). Distance magic labelings of graphs, Australasian Journal of Combinatorics, 28, 305–315.
Sankar, K., Sivakumaran, V., and Sethuraman, G. (2016). Distance magic labeling of join graph, International Journal of Pure and Applied Mathematics, 6, 19–25.
Sugeng, K. A., Froncek, D., Miller, M., Ryan, J. and Walker, J. (2009). On Distance magic labelings of graphs, Journal of Combinatorial Mathematics and Combinatorial Computing, 71, 39–48.
Vilfred, V. (1994). ∑-labelled graph and circulant graphs (Ph.D. Thesis). University of Kerala. Trivandrum. India.
West, D. B. (2001). Introduction to graph theory. Pretice Hall. New Jersey.
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Published
2021-09-15
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Research Article
