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Vertex-magic Labelings of Regular Graphs: Disjoint Unions and Assemblages

MacDougall, James A. and Gray, I. D. (2010) Vertex-magic Labelings of Regular Graphs: Disjoint Unions and Assemblages. .

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    Abstract

    We establish the existence of vertex-magic total labelings (VMTLs) for several in¯nite 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 {emp \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 $t \geq 1$. The construction also extends to certain families of non-regular graphs.

    Item Type: Article
    Subjects: 00-xx General > 00Axx General and miscellaneous specific topics
    Faculty: UNSPECIFIED
    Depositing User: Stephanie
    Date Deposited: 28 Sep 2012 12:05
    Last Modified: 28 Sep 2012 12:05
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/792

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