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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]
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Abstract

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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.

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