All Cycles are Edge-Magic

Abstract

We prove that all cycles are edge-magic, thus solving a problem presented by [2]. In [3] it was shown that all cycles of odd length are edge-magic. We give explicit constructions that show that all cycles of even length are edge-magic. Our constructions differ for the case of cycles of length $n\equiv 0(\mathrm{mod}4)$ and $n\equiv 2(\mathrm{mod}4)$.