On the existence of degree-magic labellings of the n-fold self-union of complete bipartite graphs
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Publication Details
Author list: Inpoonjai P., Jiarasuksakun T.
Publisher: Lugansk Taras Shevchenko National University
Publication year: 2019
Volume number: 28
Issue number: 1
Start page: 107
End page: 122
Number of pages: 16
ISSN: 1726-3255
eISSN: 1726-3255
Languages: English-Great Britain (EN-GB)
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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. © Journal “Algebra and Discrete Mathematics”.
Keywords
Bipartite graphs, Magic rectangles, Regular graphs, Tripartite graphs
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