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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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2019 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут прикладної математики і механіки НАН України
2019
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| Online Zugang: | 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 |
| Zitieren: | 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862654440566161408 |
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| author | Inpoonjai, P. Jiarasuksakun, T. |
| author_facet | Inpoonjai, P. Jiarasuksakun, T. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
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| first_indexed | 2025-12-02T00:31:08Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-188480 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-02T00:31:08Z |
| publishDate | 2019 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | On the existence of degree-magic labellings of the n-fold self-union of complete bipartite graphs Inpoonjai, P. Jiarasuksakun, T. |
| title | 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/188480 |
| work_keys_str_mv | AT inpoonjaip ontheexistenceofdegreemagiclabellingsofthenfoldselfunionofcompletebipartitegraphs AT jiarasuksakunt ontheexistenceofdegreemagiclabellingsofthenfoldselfunionofcompletebipartitegraphs |