Balanced degree-magic labelings of complete bipartite graphs under binary operations
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Author list: Inpoonjai P., Jiarasuksakun T.
Publication year: 2018
Journal: Iranian Journal Of Mathematical Sciences and Informatics (1735-4463)
Volume number: 13
Issue number: 2
Start page: 1
End page: 13
Number of pages: 13
ISSN: 1735-4463
Languages: English-Great Britain (EN-GB)
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Abstract
A graph is called supermagic if there is a labeling of edges where the edges are labeled with consecutive distinct positive integers such that the sum of the labels of all edges incident with any vertex is constant. A graph G is called degree-magic if there is a labeling 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 find the necessary and sufficient conditions for the existence of balanced degree-magic labelings of graphs obtained by taking the join, composition, Cartesian product, tensor product and strong product of complete bipartite graphs. © 2018 Academic Center for Education, Culture and Research TMU.
Keywords
Balanced degree-magic graphs, Complete bipartite graphs, Degree-magic graphs, Supermagic graphs
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