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A magical approach to some labeling conjectures

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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.
Opis fizyczny
  • Mathematics Department, University of Hawai'i at Hilo, 200 W. Kawili St., Hilo, HI 96720, USA
  • College of Humanities and Sciences, Nihon University, 3-25-40 Sakurajosui Setagaya-ku, Tokyo 156-8550, Japan
  • Graph Theory and Applications Research Group, School of Electrical Engineering and Computer Science, Faculty of Engineering and Built Environment, University of Newcastle, NSW 2308, Australia
  • Department of Mathematical Information Science, Faculty of Science, Tokyo University of Science, 1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan
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