a1 Departament de Matemàtica Aplicada IV, Universitat Politècnica de Catalunya, C/Esteve Terrades 5, 08860 Castelldefels, Spain (email: email@example.com)
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: firstname.lastname@example.org)
a3 Departament de Matemàtica Aplicada IV, Universitat Politècnica de Catalunya, C/Esteve Terrades 5, 08860 Castelldefels, Spain (email: email@example.com)
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
Keywords and phrases
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