Geodesic
Magic and supermagic dense bipartite graphs
Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 3, pp. 583-591

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A graph is called magic (supermagic) if it admits a labelling of the edges by pairwise different (and consecutive) positive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. In the paper we prove that any balanced bipartite graph with minimum degree greater than |V(G)|/4 ≥ 2 is magic. A similar result is presented for supermagic regular bipartite graphs.
Keywords: magic graphs, supermagic graphs, bipartite graphs 
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     author = {Ivanco, Jaroslav},
     title = {Magic and supermagic dense bipartite graphs},
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Ivanco, Jaroslav. Magic and supermagic dense bipartite graphs. Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 3, pp. 583-591. http://geodesic.mathdoc.fr/item/DMGT_2007_27_3_a15/