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Strong labelings of linear forests

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Abstract

A (p, q)-graph G is called super edge-magic if there exists a bijective function f: V (G) ∪ E(G) → {1, 2, ..., p+q} such that f(u)+f(υ)+f(uυ) is a constant for each uυ ε E(G) and f(V (G)) = {1, 2, ..., p}.

In this paper, we introduce the concept of strong super edge-magic labeling as a particular class of super edge-magic labelings and we use such labelings in order to show that the number of super edge-magic labelings of an odd union of path-like trees (mT), all of them of the same order, grows at least exponentially with m.

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Authors and Affiliations

  1. Department of Applied Mathematics, Technical University in Košice, Letná 9, 042 00, Košice, Slovakia

    Martin Bača

  2. School of Electrical Engineering and Computer Science, The University of Newcastle, Newcastle, NSW, 2308, Australia

    Yu Qing Lin

  3. Universitat Internacional de Catalunya, Barcelona, Catalunya, 08017, Spain

    Francesc A. Muntaner-Batle

  4. Departament de Matemàtica Aplicada i Telemàtica Universitat Politècnica de Catalunya, Barcelona, Catalunya, 08034, Spain

    Miquel Rius-Font

Authors
  1. Martin Bača
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  2. Yu Qing Lin
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  3. Francesc A. Muntaner-Batle
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  4. Miquel Rius-Font
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Corresponding author

Correspondence to Martin Bača.

Additional information

Supported by the Slovak VEGA (Grant No. 1/4005/07) and Spanish Research Council (Grant No. BFM2002-00412). Supported in part by Abdus Salam School of Mathematical Sciences, GC Uiversity, Lahore, Pakistan, where part of the research was conducted by the first and the third author

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Bača, M., Lin, Y.Q., Muntaner-Batle, F.A. et al. Strong labelings of linear forests. Acta. Math. Sin.-English Ser. 25, 1951–1964 (2009). https://doi.org/10.1007/s10114-009-8284-3

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  • DOI: https://doi.org/10.1007/s10114-009-8284-3

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