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On consecutive edge magic total labelings of connected bipartite graphs. (English) Zbl 1358.05246

Summary: Since J. Sedláček introduced the notion of magic labeling of a graph in [“Problem 27”, in: Theory of Graphs and its Applications. Proceedings of the Symposium held in Smolenice in June 1963. New York: Academic Press. 163–167 (1963)], a variety of magic labelings of a graph have been defined and studied. In this paper, we study consecutive edge magic labelings of a connected bipartite graph. We make a useful observation that there are only four possible values of \(b\) for which a connected bipartite graph has a \(b\)-edge consecutive magic labeling. On the basis of this fundamental result, we deduce various interesting results on consecutive edge magic labelings of bipartite graphs. As a matter of fact, we do not focus just on specific classes of graphs, but also discuss the more general classes of non-bipartite and bipartite graphs.

MSC:

05C78 Graph labelling (graceful graphs, bandwidth, etc.)
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References:

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