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 $n\ge 3$ and $k\ge 3$ 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.