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DC Field | Value | Language |
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dc.contributor.author | Simson, D. | - |
dc.date.accessioned | 2019-12-02T09:34:12Z | - |
dc.date.available | 2019-12-02T09:34:12Z | - |
dc.date.issued | 2019 | - |
dc.identifier.uri | http://hdl.handle.net/123456789/4356 | - |
dc.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 | uk_UA |
dc.description.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. | uk_UA |
dc.language.iso | en | uk_UA |
dc.publisher | ДЗ "ЛНУ імені Тараса Шевченка" | uk_UA |
dc.subject | regular graphs | uk_UA |
dc.subject | bipartite graphs | uk_UA |
dc.subject | tripartite graphs, supermagic graphs | uk_UA |
dc.subject | degree-magic graphs | uk_UA |
dc.subject | balanced degree-magic graphs | uk_UA |
dc.subject | magic rectangles | uk_UA |
dc.title | On the existence of degree-magic labellings of the n-fold self-union of complete bipartite graphs | uk_UA |
dc.type | Article | uk_UA |
Appears in Collections: | Algebra and Discrete Mathematics. - № 1 (28). - 2019 |
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374-4419-1-PB.pdf | 668.82 kB | Adobe PDF | View/Open |
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