Geodesic
On the existence of degree-magic labellings of the n-fold self-union of complete bipartite graphs
Algebra and discrete mathematics, Tome 28 (2019) no. 1, pp. 107-122.

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Magic rectangles are a classical generalization of the well-known magic squares, and they are related to graphs. A graph G is called degree-magic if there exists 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)|)deg⁡(v)/2. Degree-magic graphs extend supermagic regular graphs. In this paper, we present a general proof of the necessary and sufficient conditions for the existence of degree-magic labellings of the n-fold self-union of complete bipartite graphs. We apply this existence to construct supermagic regular graphs and to identify the sufficient condition for even n-tuple magic rectangles to exist.
Mots-clés : regular graphs, bipartite graphs, tripartite graphs, supermagic graphs, degree-magic graphs, balanced degree-magic graphs, magic rectangles. 
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Phaisatcha Inpoonjai; Thiradet Jiarasuksakun. On the existence of degree-magic labellings of the $n$-fold self-union of complete bipartite graphs. Algebra and discrete mathematics, Tome 28 (2019) no. 1, pp. 107-122. https://geodesic-test.mathdoc.fr/item/ADM_2019_28_1_a7/

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