On super edge-magic decomposable graphs

S. C. López (), F. A. Muntaner-Batle () and M. Rius-Font ()
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S. C. López: Universitat Politècnica de Catalunya
F. A. Muntaner-Batle: The University of Newcastle
M. Rius-Font: Universitat Politècnica de Catalunya

Indian Journal of Pure and Applied Mathematics, 2012, vol. 43, issue 5, 455-473

Abstract: Abstract Let G be any graph and let {H i } i∈I be a family of graphs such that $$E\left( {H_i } \right) \cap E\left( {H_j } \right) = \not 0$$ when i ≠ j, ∪ i∈I E(H i ) = E(G) and $$E\left( {H_i } \right) \ne \not 0$$ for all i ∈ I. In this paper we introduce the concept of {H i } i∈I -super edge-magic decomposable graphs and {H i } i∈I -super edge-magic labelings. We say that G is {H i } 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 H i meets the following two requirements: β(V(H i )) = {1,2,..., |V(H i )|} and {β(a) +β(b): ab ∈ E(H i )} is a set of consecutive integers. Such function β is called an {H i } i∈I -super edge-magic labeling of G. We characterize the set of cycles C n which are {H 1, H 2}-super edge-magic decomposable when both, H 1 and H 2 are isomorphic to (n/2)K 2. New lines of research are also suggested.

Keywords: Super edge-magic decomposable; ⋇ h -product (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s13226-012-0028-x

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