Edge-magic and Vertex-magic Total Labelings of Certain Cycles

Abstract

We provide many new edge-magic and vertex-magic total labelings for the cycles \(C_{nk}\), where \(n \geq 3\) and \(k \geq 3\) are both integers and \(n\) is odd. Our techniques are of interest since known labelings for \(C_{k}\) are used in the construction of those for \(C_{nk}\). This provides significant new evidence for a conjecture on the possible magic constants for edge-magic and vertex-magic cycles.