Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-29T17:08:39.088Z Has data issue: false hasContentIssue false
  • English
  • Français

BI-MAGIC AND OTHER GENERALIZATIONS OF SUPER EDGE-MAGIC LABELINGS

Part of: Graph theory

Published online by Cambridge University Press:  15 June 2011

S. C. LÓPEZ ,
F. A. MUNTANER-BATLE  and
M. RIUS-FONT
S. C. LÓPEZ*
Affiliation:
Departament de Matemàtica Aplicada IV, Universitat Politècnica de Catalunya, C/Esteve Terrades 5, 08860 Castelldefels, Spain (email: [email protected])
F. A. MUNTANER-BATLE
Affiliation:
Graph Theory and Applications Research Group, School of Electrical Engineering and Computer Science, Faculty of Engineering and Built Environment, The University of Newcastle, NSW 2308, Australia (email: [email protected])
M. RIUS-FONT
Affiliation:
Departament de Matemàtica Aplicada IV, Universitat Politècnica de Catalunya, C/Esteve Terrades 5, 08860 Castelldefels, Spain (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, we use the product ⊗h in order to study super edge-magic labelings, bi-magic labelings and optimal k-equitable labelings. We establish, with the help of the product ⊗h, new relations between super edge-magic labelings and optimal k-equitable labelings and between super edge-magic labelings and edge bi-magic labelings. We also introduce new families of graphs that are inspired by the family of generalized Petersen graphs. The concepts of super bi-magic and r-magic labelings are also introduced and discussed, and open problems are proposed for future research.

Keywords

super edge-magicbi-magick-equitable

MSC classification

Secondary: 05C78: Graph labelling (graceful graphs, bandwidth, etc.)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 84 , Issue 1 , August 2011 , pp. 137 - 152
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

Footnotes

The research conducted in this document by first and third author has been supported by the Spanish Research Council under project MTM2008-06620-C03-01 and by the Catalan Research Council under grant 2009SGR1387.

References

[1]Acharya, B. D. and Hegde, S. M., ‘Strongly indexable graphs’, Discrete Math. 93 (1991), 123–129.CrossRefGoogle Scholar
[2]Barrientos, C., ‘Difference vertex labelings’, PhD Thesis, Universitat Politècnica de Catalunya, 2004.Google Scholar
[3]Barrientos, C., Dejter, I. J. and Hevia, H., ‘Equitable labelings of forests’, in: Combinatorics and Graph Theory’95, Vol.1 (ed. Alavi, Y.) (World Scientific, Singapore, 1995), pp. 1–26.Google Scholar
[4]Bloom, G. and Ruiz, S., ‘Decomposition into linear forest and difference labelings of graphs’, Discrete Appl. Math. 49 (1994), 13–37.CrossRefGoogle Scholar
[5]Chartrand, G. and Lesniak, L., Graphs and Digraphs, 2nd edn (Wadsworth & Brooks/Cole Advanced Books and Software, Monterey, 1986).Google Scholar
[6]Enomoto, H., Lladó, A., Nakamigawa, T. and Ringel, G., ‘Super edge-magic graphs’, SUT J. Math. 34 (1998), 105–109.CrossRefGoogle Scholar
[7]Figueroa-Centeno, R. M., Ichishima, R. and Muntaner-Batle, F. A., ‘The place of super edge-magic labelings among other classes of labelings’, Discrete Math. 231(1–3) (2001), 153–168.CrossRefGoogle Scholar
[8]Figueroa-Centeno, R. M., Ichishima, R., Muntaner-Batle, F. A. and Rius-Font, M., ‘Labeling generating matrices’, J. Combin. Math. Combin. Comput. 67 (2008), 189–216.Google Scholar
[9]Gallian, J. A., ‘A dynamic survey of graph labeling’, Electron. J. Combin. 17 (2010), #DS6.Google Scholar
[10]Kotzig, A. and Rosa, A., ‘Magic valuations of finite graphs’, Canad. Math. Bull. 13 (1970), 451–461.CrossRefGoogle Scholar
[11]Rajan, B., Rajasingh, I. and Basker, M. A., ‘Edge bi-magic total labelings of graphs’, Proc. 5th Asian Mathematical Conf., Malaysia, June 2009 (eds. L. S. Keong and H. K. Haith) (June 2009), pp. 426–428.Google Scholar
[12]Valdés, L., ‘Edge-magic K p’. Paper delivered at Thirty-Second South Eastern International Conference on Combinatorics, Graph Theory and Computing, Baton Rouge, 2001.Google Scholar
[13]Wallis, W. D., Magic Graphs (Birkhäuser, Boston, MA, 2001).CrossRefGoogle Scholar
[14]West, D. B., Introduction to Graph Theory (Prentice Hall, Upper Saddle River, NJ, 1996).Google Scholar
[15]Wojciechowski, J., ‘Long induced cycles in the hypercube and colourings of graphs’, PhD Thesis, University of Cambridge, 1990.Google Scholar
[16]Wojciechowski, J., ‘Equitable labelings of cycles’, J. Graph Theory 17 (1993), 531–547.CrossRefGoogle Scholar