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2011 | 31 | 1 | 79-113
Tytuł artykułu

A magical approach to some labeling conjectures

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Wydawca
Rocznik
Tom
31
Numer
1
Strony
79-113
Opis fizyczny
Daty
wydano
2011
otrzymano
2009-09-21
poprawiono
2010-04-06
zaakceptowano
2010-04-06
Twórcy
  • 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
autor
  • Department of Mathematical Information Science, Faculty of Science, Tokyo University of Science, 1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan
Bibliografia
  • [1] J. Abrham and A. Kotzig, Graceful valuations of 2-regular graphs with two components, Discrete Math. 150 (1996) 3-15, doi: 10.1016/0012-365X(95)00171-R.
  • [2] G. Chartrand and L. Lesniak, Graphs and Digraphs (Wadsworth & Brook/Cole Advanced Books and Software, Monterey, Calif. 1986).
  • [3] H. Enomoto, A. Lladó, T. Nakamigawa and G. Ringel, Super edge-magic graphs, SUT J. Math. 34 (1998) 105-109.
  • [4] R.M. Figueroa-Centeno, R. Ichishima and F.A. Muntaner-Batle, The place of super edge-magic labelings among other classes of labelings, Discrete Math. 231 (2001) 153-168, doi: 10.1016/S0012-365X(00)00314-9.
  • [5] R.M. Figueroa-Centeno, R. Ichishima and F.A. Muntaner-Batle, On super edge-magic graphs, Ars Combin. 64 (2002) 81-96.
  • [6] R.M. Figueroa-Centeno, R. Ichishima and F.A. Muntaner-Batle, Labeling the vertex amalgamation of graphs, Discuss. Math. Graph Theory 23 (2003) 129-139, doi: 10.7151/dmgt.1190.
  • [7] R.M. Figueroa-Centeno, R. Ichishima and F.A. Muntaner-Batle, On edge-magic labelings of certain disjoint unions of graphs, Austral. J. Combin. 32 (2005) 225-242.
  • [8] R.M. Figueroa-Centeno, R. Ichishima and F.A. Muntaner-Batle, On the super edge-magic deficiency of graphs, Ars Combin. 78 (2006) 33-45.
  • [9] R.M. Figueroa-Centeno, R. Ichishima, F.A. Muntaner-Batle and M. Rius-Font, Labeling generating matrices, J. Combin. Math. Combin. Comput. 67 (2008) 189-216.
  • [10] R. Frucht and L.C. Salinas, Graceful numbering of snakes with constraints on the first label, Ars Combin. (B) 20 (1985) 143-157.
  • [11] J.A. Gallian, A dynamic survey of graph labeling, Electron. J. Combin. 5 (2009) #DS6.
  • [12] S.W. Golomb, How to number a graph, in: Graph Theory and Computing, R.C. Read, ed. (Academic Press, New York, 1972) 23-37.
  • [13] T. Grace, On sequential labelings of graphs, J. Graph Theory 7 (1983) 195-201, doi: 10.1002/jgt.3190070208.
  • [14] R.L. Graham and N.J. Sloane, On additive bases and harmonious graphs, SIAM J. Alg. Discrete Meth. 1 (1980) 382-404, doi: 10.1137/0601045.
  • [15] I. Gray and J.A. MacDougall, Vertex-magic labelings of regular graphs II, Discrete Math. 309 (2009) 5986-5999, doi: 10.1016/j.disc.2009.04.031.
  • [16] J. Holden, D. McQuillan and J.M. McQuillan, A conjecture on strong magic labelings of 2-regular graphs, Discrete Math. 309 (2009) 4130-4136, doi: 10.1016/j.disc.2008.12.020.
  • [17] A. Kotzig, β-valuations of quadratic graphs with isomorphic components, Utilitas Math. 7 (1975) 263-279.
  • [18] A. Kotzig and A. Rosa, Magic valuations of finite graphs, Canad. Math. Bull. 13 (1970) 451-461, doi: 10.4153/CMB-1970-084-1.
  • [19] S.M. Lee, E. Schmeichel and S.C. Shee, On felicitous graphs, Discrete Math. 93 (1991) 201-209, doi: 10.1016/0012-365X(91)90256-2.
  • [20] M. Seoud, A.E.I. Abdel Maqsoud and J. Sheehan, Harmonious graphs, Utilitas Math. 47 (1995) 225-233.
  • [21] S.C. Shee, On harmonious and related graphs, Ars Combin. 23 (1987) 237-247.
  • [22] S.C. Shee and S.M. Lee, On harmonious and felicitous labelings of graphs, Congress Numer. 68 (1989) 155-170.
  • [23] G. Ringel and A. Lladó, Another tree conjecture, Bull. Inst. Combin. Appl. 18 (1996) 83-85.
  • [24] A. Rosa, On certain valuations of the vertices of a graph, Theory of Graphs (Internat. Symposium, Rome, July 1966), Gordon and Breach, N.Y and Dunod Paris (1967) 349-355.
  • [25] W.D. Wallis, Magic Graphs (Birkhäuser, Boston, 2001), doi: 10.1007/978-1-4612-0123-6.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1531
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