Abstract: “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 is 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. In this paper we generalize magic rectangles to be n -tuple magic rectangles, and prove the necessary and sufficient conditions for the existence of even n - tuple magic rectangles. Using this existence we identify the sufficient condition for degree-magic labellings of the n -fold selfunion of complete bipartite graphs to exist.”

Keywords: magic squares, magic rectangles, degree-magic graphs