Vertex-magic labeling of regular graphs: Disjoint unions and assemblages

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 an...

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Bibliographic Details
Published in:Discrete Applied Mathematics 2012-05, Vol.160 (7-8), p.1114-1125
Main Authors: Gray, I.D., MacDougall, J.A.
Format: Article
Language:English
Subjects:
Construction
Disengaging
Graphs
Magic labeling
Marking
Mathematical analysis
Proving
Reproduction
Unions
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Summary: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.
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2011.11.025