On super edge-magic decomposable graphs

López Masip, Susana-Clara; Muntaner Batle, F. A.; Rius Font, Miquel

doi:https://doi.org/10.1007/s13226-012-0028-x

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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.

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

Is part of

Indian Journal of Pure & Applied Mathematics, 2012, vol. 43, num. 5, p. 455-473