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 \(1,2,\dots,|E(G)|\) such that the sum of the labels of the edges incident with any vertex \(v\)...
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| Date: | 2019 |
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| Language: | English |
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Lugansk National Taras Shevchenko University
2019
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/374 |
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| Journal Title: | Algebra and Discrete Mathematics |
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admjournalluguniveduua-article-3742019-10-20T08:14:09Z On the existence of degree-magic labellings of the \(n\)-fold self-union of complete bipartite graphs Inpoonjai, Phaisatcha Jiarasuksakun, Thiradet regular graphs, bipartite graphs, tripartite graphs, supermagic graphs, degree-magic graphs, balanced degree-magic graphs, magic rectangles 05C78; 05B15 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 \(1,2,\dots,|E(G)|\) 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. Lugansk National Taras Shevchenko University 2019-10-20 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/374 Algebra and Discrete Mathematics; Vol 28, No 1 (2019) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/374/pdf Copyright (c) 2019 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
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| datestamp_date |
2019-10-20T08:14:09Z |
| collection |
OJS |
| language |
English |
| topic |
regular graphs bipartite graphs tripartite graphs supermagic graphs degree-magic graphs balanced degree-magic graphs magic rectangles 05C78 05B15 |
| spellingShingle |
regular graphs bipartite graphs tripartite graphs supermagic graphs degree-magic graphs balanced degree-magic graphs magic rectangles 05C78 05B15 Inpoonjai, Phaisatcha Jiarasuksakun, Thiradet On the existence of degree-magic labellings of the \(n\)-fold self-union of complete bipartite graphs |
| topic_facet |
regular graphs bipartite graphs tripartite graphs supermagic graphs degree-magic graphs balanced degree-magic graphs magic rectangles 05C78 05B15 |
| format |
Article |
| author |
Inpoonjai, Phaisatcha Jiarasuksakun, Thiradet |
| author_facet |
Inpoonjai, Phaisatcha Jiarasuksakun, Thiradet |
| author_sort |
Inpoonjai, Phaisatcha |
| 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 |
| 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 \(1,2,\dots,|E(G)|\) 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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2019 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/374 |
| work_keys_str_mv |
AT inpoonjaiphaisatcha ontheexistenceofdegreemagiclabellingsofthenfoldselfunionofcompletebipartitegraphs AT jiarasuksakunthiradet ontheexistenceofdegreemagiclabellingsofthenfoldselfunionofcompletebipartitegraphs |
| first_indexed |
2025-12-02T15:40:15Z |
| last_indexed |
2025-12-02T15:40:15Z |
| _version_ |
1850412159407751168 |