Geodesic
A magical approach to some labeling conjectures
Discussiones Mathematicae. Graph Theory, Tome 31 (2011) no. 1, pp. 79-113

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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 
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Figueroa-Centeno, Ramon; Ichishima, Rikio; Muntaner-Batle, Francesc; Oshima, Akito. A magical approach to some labeling conjectures. Discussiones Mathematicae. Graph Theory, Tome 31 (2011) no. 1, pp. 79-113. http://geodesic.mathdoc.fr/item/DMGT_2011_31_1_a5/