Perfect (super) Edge-Magic Crowns

View/ Open
Issue date
2017Suggested citation
López Masip, Susana-Clara;
Muntaner Batle, Francesc Antoni;
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.
Metadata
Show full item recordAbstract
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.