Cited By
View all- Chen GLi WZhong MXin B(2022)On the Existence of Regular Sparse Anti-magic Squares of Odd OrderGraphs and Combinatorics10.1007/s00373-021-02437-z38:2Online publication date: 1-Feb-2022
Vertex-magic labeling of regular graphs: Disjoint unions and assemblages
Pages 1114 - 1125
Abstract
We establish the existence of vertex-magic total labelings (VMTLs) for several infinite classes of regular graphs. The main method of construction is to assemble a number of appropriately labeled copies of one graph into a single graph with a VMTL. This method enables us for example to begin with any even-regular graph and from it construct a cubic graph possessing a VMTL. An important feature of the construction is that it produces strong VMTLs for many even order regular graphs. In addition the method provides another proof that for any odd-regular graph G possessing a VMTL, the disconnected graph tG has a VMTL for all t>=1. The construction also extends to certain families of non-regular graphs.
References
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Gray, I.D. and MacDougall, J.A., Vertex-magic labeling of non-regular graphs. Australas. J. Combin. v46. 173-183.
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- Vertex-magic labeling of regular graphs: Disjoint unions and assemblages
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Copyright © Elsevier B.V. © 2011.
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Elsevier Science Publishers B. V.
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Published: 01 May 2012
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Cited By
View all- Chen GLi WZhong MXin B(2022)On the Existence of Regular Sparse Anti-magic Squares of Odd OrderGraphs and Combinatorics10.1007/s00373-021-02437-z38:2Online publication date: 1-Feb-2022