Perfect (super) edge-magic crowns

Abstract

In this paper we continue the study of the valences for (super) edge-magic labelings of crowns $C_m\odot {\overline{K}}_n$ 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 $C_m\odot {\overline{K}}_n$, in terms of the prime factors of $m$.

11 pages, 2 figures