Discussiones Mathematicae Graph Theory 31(1) (2011)
79-113
DOI: https://doi.org/10.7151/dmgt.1531
A MAGICAL APPROACH TO SOME LABELING CONJECTURES
Ramon M. Figueroa-Centeno
Mathematics Department, University of Hawai'i at Hilo | Rikio Ichishima
College of Humanities and Sciences, Nihon University | Francesc A. Muntaner-Batle
Graph Theory and Applications Research Group | Akito Oshima
Department of Mathematical Information Science |
Abstract
In this paper, a complete characterization of the (super) edge-magic linear forests with two components is provided. In the process of establishing this characterization, the super edge-magic, harmonious, sequential and felicitous properties of certain 2-regular graphs are investigated, and several results on super edge-magic and felicitous labelings of unions of cycles and paths are presented. These labelings resolve one conjecture on harmonious graphs as a corollary, and make headway towards the resolution of others. They also provide the basis for some new conjectures (and a weaker form of an old one) on labelings of 2-regular graphs.Keywords: edge-magic labelling, edge-magic total labelling, felicitous labelling, harmonious labelling, sequential labelling.
2010 Mathematics Subject Classification: 05C78.
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Received 21 September 2009
Revised 6 April 2010
Accepted 6 April 2010
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