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Algebra and Discrete Mathematics, 2019, Volume 28, Issue 1, Pages 107–122
(Mi adm717)
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This article is cited in 1 scientific paper (total in 1 paper)
RESEARCH ARTICLE
On the existence of degree-magic labellings of the $n$-fold self-union of complete bipartite graphs
Phaisatcha Inpoonjaia, Thiradet Jiarasuksakunb a Faculty of Sciences and Agricultural Technology, Rajamangala University of Technology Lanna Chiangrai, 99, Sai Khao, Phan District, Chiang Rai, 57120, Thailand
b Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi, 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, Thailand
Abstract:
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.
Keywords:
regular graphs, bipartite graphs, tripartite graphs, supermagic graphs, degree-magic graphs, balanced degree-magic graphs, magic rectangles.
Received: 28.12.2016 Revised: 07.03.2017
Citation:
Phaisatcha Inpoonjai, Thiradet Jiarasuksakun, “On the existence of degree-magic labellings of the $n$-fold self-union of complete bipartite graphs”, Algebra Discrete Math., 28:1 (2019), 107–122
Linking options:
https://www.mathnet.ru/eng/adm717 https://www.mathnet.ru/eng/adm/v28/i1/p107
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Abstract page: | 133 | Full-text PDF : | 51 | References: | 30 |
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