Geodesic
A characterization of complete tripartite degree-magic graphs
Discussiones Mathematicae. Graph Theory, Tome 32 (2012) no. 2, pp. 243-253

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A graph is called degree-magic if it admits a labelling of the edges by integers 1, 2,..., |E(G)| such that the sum of the labels of the edges incident with any vertex v is equal to (1+ |E(G)|)/2*deg(v). Degree-magic graphs extend supermagic regular graphs. In this paper we characterize complete tripartite degree-magic graphs.
Keywords: supermagic graphs, degree-magic graphs, complete tripartite graphs 
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Bezegová, Ľudmila; Ivančo, Jaroslav. A characterization of complete tripartite degree-magic graphs. Discussiones Mathematicae. Graph Theory, Tome 32 (2012) no. 2, pp. 243-253. http://geodesic.mathdoc.fr/item/DMGT_2012_32_2_a3/