Perfect (super) Edge-Magic Crowns

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Issue date
2017
Author
López Masip, Susana-Clara
Muntaner Batle, F. A.
Prabu, M.
Suggested citation
López Masip, Susana-Clara; Muntaner Batle, F. A.; Prabu, M.; . (2017) . Perfect (super) Edge-Magic Crowns. Results in Mathematics, 2017, vol. 71, num. 3-4, p. 1459-1471. https://doi.org/10.1007/s00025-016-0643-7.
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Abstract
A graph G is called edge-magic if there is a bijective function f from the set of vertices and edges to the set {1,2, ,|V(G)|+|E(G)|} such that the sum f(x)+f(xy)+f(y) for any xy in E(G) is constant. Such a function is called an edge-magic labelling of G and the constant is called the valence. An edge-magic labelling with the extra property that f(V(G))={1,2, ,|V(G)|} is called super edge-magic. A graph is called perfect (super) edge-magic if all theoretical (super) edge-magic valences are possible. In this paper we continue the study of the valences for (super) edge-magic labelings of crowns Cm⊙K¯¯¯¯¯n and we prove that the crowns are perfect (super) edge-magic when m=pq where p and q are different odd primes. We also provide a lower bound for the number of different valences of Cm⊙K¯¯¯¯¯n , in terms of the prime factors of m.
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http://hdl.handle.net/10459.1/66441
DOI
https://doi.org/10.1007/s00025-016-0643-7
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Results in Mathematics, 2017, vol. 71, num. 3-4, p. 1459-1471
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