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On the existence of degree-magic labellings of the n-fold self-union of complete bipartite graphs
Репозиторій DSpace/Manakin
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On the existence of degree-magic labellings of the n-fold self-union of complete bipartite graphs
Інший ID:
2010 MSC: Primary 05C78; Secondary 05B15.
Посилання:
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.
Підтримка:
The authors would like to thank the anonymous referee for careful reading and the helpful comments improving this paper.
Дата:
2019
Переглядів:
259
Завантажень:
73
Анотація:
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.
