Vertex-magic labelings of regular graphs II

Title: Vertex-magic labelings of regular graphs II
Creator: Gray, I. D.; MacDougall, James A.
Relation: Discrete Mathematics Vol. 309, Issue 20, p. 5986-5999
Publisher Link: http://dx.doi.org/10.1016/j.disc.2009.04.031
Publisher: Elsevier
Resource Type: journal article
Date: 2009
Description: Previously the first author has shown how to construct vertex-magic total labelings (VMTLs) for large families of regular graphs. The construction proceeds by successively adding arbitrary 2-factors to a regular graph of order n which possesses a strong VMTL, to produce a regular graph of the same order but larger size. In this paper, we exploit this construction method. We are able to show that for any r ≥ 4, every r-regular graph of odd order n ≤ 17 has a strong VMTL. We show how to produce strong labelings for some families of 2-regular graphs since these are used as the starting points of our construction. While even-order regular graphs are much harder to deal with, we introduce ‘mirror’ labelings which provide a suitable starting point from which the construction can proceed. We are able to show that several large classes of r-regular graphs of even order (including some Hamiltonian graphs) have VMTLs.
Subject: magic labeling
Identifier: http://hdl.handle.net/1959.13/915980
Identifier: uon:7865
Identifier: ISSN:0012-365X
Language: eng
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