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Title: | On the existence of degree-magic labellings of the n-fold self-union of complete bipartite graphs |
Authors: | Simson, D. |
Keywords: | regular graphs bipartite graphs tripartite graphs, supermagic graphs degree-magic graphs balanced degree-magic graphs magic rectangles |
Issue Date: | 2019 |
Publisher: | ДЗ "ЛНУ імені Тараса Шевченка" |
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 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. |
Description: | Simson D. On the existence of degree-magic labellings of the n-fold self-union of complete bipartite graphs / D.Simson // Algebra and Discrete Mathematics. - 2019. - Vol. 28. - Number 1. - Рp.107-122 |
URI: | http://hdl.handle.net/123456789/4356 |
Appears in Collections: | Algebra and Discrete Mathematics. - № 1 (28). - 2019 |
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