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On super edge-magic decomposable graphs

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Issue date
2012
Author
López Masip, Susana-Clara
Muntaner Batle, F. A.
Rius Font, Miquel
Suggested citation
López Masip, Susana-Clara; Muntaner Batle, F. A.; Rius Font, Miquel; . (2012) . On super edge-magic decomposable graphs. Indian Journal of Pure & Applied Mathematics, 2012, vol. 43, num. 5, p. 455-473. https://doi.org/10.1007/s13226-012-0028-x.
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Abstract
Let G be any graph and let {Hi}i∈I be a family of graphs such that E(Hi) ∩ E(Hj ) = ∅ when i 6= j, ∪i∈IE(Hi) = E(G) and E(Hi) 6= ∅ for all i ∈ I. In this paper we introduce the concept of {Hi}i∈I -super edge-magic decomposable graphs and {Hi}i∈I -super edge-magic labelings. We say that G is {Hi}i∈I -super edge-magic decomposable if there is a bijection β : V (G) → {1, 2, . . . , |V (G)|} such that for each i ∈ I the subgraph Hi meets the following two requirements: β(V (Hi)) = {1, 2, . . . , |V (Hi)|} and {β(a) + β(b) : ab ∈ E(Hi)} is a set of consecutive integers. Such function β is called an {Hi}i∈I -super edge-magic labeling of G. We characterize the set of cycles Cn which are {H1, H2}-super edge-magic decomposable when both, H1 and H2 are isomorphic to (n/2)K2. New lines of research are also suggested.
URI
http://hdl.handle.net/10459.1/66517
DOI
https://doi.org/10.1007/s13226-012-0028-x
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Indian Journal of Pure & Applied Mathematics, 2012, vol. 43, num. 5, p. 455-473
European research projects
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  • Publicacions de projectes de recerca del Plan Nacional [2217]
  • Articles publicats (Matemàtica) [266]

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  • Labeling constructions using digraph products 

    López Masip, Susana-Clara; Muntaner Batle, F. A.; Rius Font, Miquel (Elsevier, 2013)
    In this paper we study the edge-magicness of graphs with equal size and order, and we use such graphs and digraph products in order to construct labelings of different classes and of different graphs. We also study super ...
  • The power of digraph products applied to labelings 

    Ichishima, R.; López Masip, Susana-Clara; Muntaner Batle, F. A.; Rius Font, Miquel (Elsevier, 2012)
    The ⊗h-product was introduced in 2008 by Figueroa-Centeno et al. as a way to construct new families of (super) edge-magic graphs and to prove that some of those families admit an exponential number of (super) edge-magic ...
  • A new labeling construction from the ⊗h-product 

    López Masip, Susana-Clara; Muntaner Batle, F. A.; Prabu, M. (Elsevier, 2017)
    The -product that is referred in the title was introduced in 2008 as a generalization of the Kronecker product of digraphs. Many relations among labelings have been obtained since then, always using as a second factor a ...

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