On the existence of degree-magic labellings of the n-fold self-union of complete bipartite graphs
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...
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| Опубліковано в: : | Algebra and Discrete Mathematics |
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| Дата: | 2019 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2019
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/188480 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On the existence of degree-magic labellings of the n-fold self-union of complete bipartite graphs / P. Inpoonjai, T. Jiarasuksakun // Algebra and Discrete Mathematics. — 2019. — Vol. 28, № 1. — С. 107–122. — Бібліогр.: 15 назв. — англ. |
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nasplib_isofts_kiev_ua-123456789-188480 |
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Inpoonjai, P. Jiarasuksakun, T. 2023-03-02T15:26:44Z 2023-03-02T15:26:44Z 2019 On the existence of degree-magic labellings of the n-fold self-union of complete bipartite graphs / P. Inpoonjai, T. Jiarasuksakun // Algebra and Discrete Mathematics. — 2019. — Vol. 28, № 1. — С. 107–122. — Бібліогр.: 15 назв. — англ. 1726-3255 2010 MSC: Primary 05C78; Secondary 05B15. https://nasplib.isofts.kiev.ua/handle/123456789/188480 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. The authors would like to thank the anonymous referee for careful reading and the helpful comments improving this paper. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On the existence of degree-magic labellings of the n-fold self-union of complete bipartite graphs Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
On the existence of degree-magic labellings of the n-fold self-union of complete bipartite graphs |
| spellingShingle |
On the existence of degree-magic labellings of the n-fold self-union of complete bipartite graphs Inpoonjai, P. Jiarasuksakun, T. |
| title_short |
On the existence of degree-magic labellings of the n-fold self-union of complete bipartite graphs |
| title_full |
On the existence of degree-magic labellings of the n-fold self-union of complete bipartite graphs |
| title_fullStr |
On the existence of degree-magic labellings of the n-fold self-union of complete bipartite graphs |
| title_full_unstemmed |
On the existence of degree-magic labellings of the n-fold self-union of complete bipartite graphs |
| title_sort |
on the existence of degree-magic labellings of the n-fold self-union of complete bipartite graphs |
| author |
Inpoonjai, P. Jiarasuksakun, T. |
| author_facet |
Inpoonjai, P. Jiarasuksakun, T. |
| publishDate |
2019 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| description |
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.
|
| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/188480 |
| citation_txt |
On the existence of degree-magic labellings of the n-fold self-union of complete bipartite graphs / P. Inpoonjai, T. Jiarasuksakun // Algebra and Discrete Mathematics. — 2019. — Vol. 28, № 1. — С. 107–122. — Бібліогр.: 15 назв. — англ. |
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AT inpoonjaip ontheexistenceofdegreemagiclabellingsofthenfoldselfunionofcompletebipartitegraphs AT jiarasuksakunt ontheexistenceofdegreemagiclabellingsofthenfoldselfunionofcompletebipartitegraphs |
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2025-12-02T00:31:08Z |
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2025-12-02T00:31:08Z |
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