Bulletin of the Australian Mathematical Society

Research Article

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

S. C. LÓPEZa1 c1, F. A. MUNTANER-BATLEa2 and M. RIUS-FONTa3

a1 Departament de Matemàtica Aplicada IV, Universitat Politècnica de Catalunya, C/Esteve Terrades 5, 08860 Castelldefels, Spain (email: susana@ma4.upc.edu)

a2 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: famb1es@yahoo.es)

a3 Departament de Matemàtica Aplicada IV, Universitat Politècnica de Catalunya, C/Esteve Terrades 5, 08860 Castelldefels, Spain (email: mrius@ma4.upc.edu)

Abstract

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.

(Received November 27 2010)

(Online publication June 15 2011)

2010 Mathematics subject classification

  • primary 05C78

Keywords and phrases

  • super edge-magic;
  • bi-magic;
  • k-equitable

Correspondence:

c1 For correspondence; e-mail: susana@ma4.upc.edu

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.

Dedicated to the memory of Professor Gary Bloom