All Cycles are Edge-Magic

Omer Berkman1, Michal Parnas1, Yehuda Roditty1
1The Academic College of Tel-Aviv-Yaffo Tel-Aviv, Israel.

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 \(n \equiv 0 \pmod{4}\) and \(n \equiv 2 \pmod{4}\).