Perfect (super) EdgeMagic Crowns
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2017Suggested citation
López Masip, SusanaClara;
Muntaner Batle, F. A.;
Prabu, M.;
.
(2017)
.
Perfect (super) EdgeMagic Crowns.
Results in Mathematics, 2017, vol. 71, num. 34, p. 14591471.
https://doi.org/10.1007/s0002501606437.
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A graph G is called edgemagic 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 edgemagic labelling of G and the constant is called the valence. An edgemagic labelling with the extra property that f(V(G))={1,2, ,V(G)} is called super edgemagic. A graph is called perfect (super) edgemagic if all theoretical (super) edgemagic valences are possible. In this paper we continue the study of the valences for (super) edgemagic labelings of crowns Cm⊙K¯¯¯¯¯n and we prove that the crowns are perfect (super) edgemagic 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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Results in Mathematics, 2017, vol. 71, num. 34, p. 14591471European research projects
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