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 \(n \equiv 0 \pmod{4}\) and \(n \equiv 2 \pmod{4}\).
Citation
Omer Berkman, Michal Parnas, Yehuda Roditty. All Cycles are Edge-Magic[J], Ars Combinatoria, Volume 059. 145-151. .