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

  • A. AHMAD (a1), S. C. LÓPEZ (a2), F. A. MUNTANER-BATLE (a3) and M. RIUS-FONT (a4)

Abstract

A super edge-magic labeling of a graph G=(V,E) of order p and size q is a bijection f:VE→{i}p+qi=1 such that: (1) f(u)+f(uv)+f(v)=k for all uvE; 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 uvE(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.

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Copyright

Corresponding author

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

Footnotes

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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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References

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[9]Figueroa-Centeno, R. M., Ichishima, R. and Muntaner-Batle, F. A., ‘The place of super edge-magic labeling among other classes of labeling’, Discrete Math. 231 (2001), 153168.
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ENUMERATING SUPER EDGE-MAGIC LABELINGS FOR THE UNION OF NONISOMORPHIC GRAPHS

  • A. AHMAD (a1), S. C. LÓPEZ (a2), F. A. MUNTANER-BATLE (a3) and M. RIUS-FONT (a4)

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