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Vertex-magic labelings of regular graphs II
- Source :
- Discrete Mathematics. (20):5986-5999
- Publisher :
- Elsevier B.V.
-
Abstract
- 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 [email protected]?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.
Details
- Language :
- English
- ISSN :
- 0012365X
- Issue :
- 20
- Database :
- OpenAIRE
- Journal :
- Discrete Mathematics
- Accession number :
- edsair.doi.dedup.....72a8cf95af7b181fa0569aa66ab0b5ec
- Full Text :
- https://doi.org/10.1016/j.disc.2009.04.031