On the existence of degree-magic labellings of the \(n\)-fold self-union of complete bipartite graphs

• Date: 2019
• Main Authors: Inpoonjai, Phaisatcha, Jiarasuksakun, Thiradet
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2019
• Subjects: regular graphs; bipartite graphs; tripartite graphs; supermagic graphs; degree-magic graphs; balanced degree-magic graphs; magic rectangles; 05C78; 05B15
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/374
• Journal Title: Algebra and Discrete Mathematics

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 \(v\)...