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ENUMERATING SUPER EDGE-MAGIC LABELINGS FOR THE UNION OF NONISOMORPHIC GRAPHS

Part of: Graph theory

Published online by Cambridge University Press:  15 June 2011

A. AHMAD ,
S. C. LÓPEZ ,
F. A. MUNTANER-BATLE  and
M. RIUS-FONT
A. AHMAD
Affiliation:
Department of Mathematics, Govt. College University, Lahore, Pakistan (email: ahmadsms@gmail.com)
S. C. LÓPEZ*
Affiliation:
Departament de Matemàtica Aplicada IV, Universitat Politècnica de Catalunya, C/Esteve Terrades 5, 08860 Castelldefels, Spain (email: susana@ma4.upc.edu)
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: famb1es@yahoo.es)
M. RIUS-FONT
Affiliation:
Departament de Matemàtica Aplicada IV, Universitat Politècnica de Catalunya, C/Esteve Terrades 5, 08860 Castelldefels, Spain (email: mrius@ma4.upc.edu)
*
✉For correspondence; e-mail: susana@ma4.upc.edu
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Abstract

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A super edge-magic labeling of a graph G=(V,E) of order p and size q is a bijection f:V ∪E→{i}p+qi=1 such that: (1) f(u)+f(uv)+f(v)=k for all uv∈E; and (2) f(V )={i}pi=1. Furthermore, when G is a linear forest, the super edge-magic labeling of G is called strong if it has the extra property that if uv∈E(G) , u′,v′ ∈V (G) and dG (u,u′ )=dG (v,v′ )<+∞, then f(u)+f(v)=f(u′ )+f(v′ ). In this paper we introduce the concept of strong super edge-magic labeling of a graph G with respect to a linear forest F, and we study the super edge-magicness of an odd union of nonnecessarily isomorphic acyclic graphs. Furthermore, we find exponential lower bounds for the number of super edge-magic labelings of these unions. The case when G is not acyclic will be also considered.

Keywords

super edge-magic labelingstrong super edge-magic labeling

MSC classification

Secondary: 05C78: Graph labelling (graceful graphs, bandwidth, etc.)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 84 , Issue 2 , October 2011 , pp. 310 - 321
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

Footnotes

The research conducted in this document by second and forth 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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