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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| Дата: | 2019 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2019
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-188480 |
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irk-123456789-1884802023-03-03T01:27:13Z On the existence of degree-magic labellings of the n-fold self-union of complete bipartite graphs Inpoonjai, P. Jiarasuksakun, T. 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. 2019 Article 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. http://dspace.nbuv.gov.ua/handle/123456789/188480 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Inpoonjai, P. Jiarasuksakun, T. |
| spellingShingle |
Inpoonjai, P. Jiarasuksakun, T. On the existence of degree-magic labellings of the n-fold self-union of complete bipartite graphs Algebra and Discrete Mathematics |
| author_facet |
Inpoonjai, P. Jiarasuksakun, T. |
| author_sort |
Inpoonjai, P. |
| title |
On the existence of degree-magic labellings of the n-fold self-union of complete bipartite graphs |
| 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 |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2019 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT inpoonjaip ontheexistenceofdegreemagiclabellingsofthenfoldselfunionofcompletebipartitegraphs AT jiarasuksakunt ontheexistenceofdegreemagiclabellingsofthenfoldselfunionofcompletebipartitegraphs |
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2023-10-18T23:08:27Z |
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2023-10-18T23:08:27Z |
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1796157352589656064 |