Vertex-Magic Daisy Cunningham Vertex-magic labelings are a very interesting topic in graph theory. Some very intriguing properties surface when applying vertex-magic labeling to cycle graphs. This paper will explore some of these properties. The vertex-magic labeling of a cycle graph with an odd number of vertices is very different from that of a cycle graph with an even number of vertices. In this paper, we will present bounds for the magic number of any given cycle graph as well as algorithms for producing vertex-magic graphs with magic numbers equal to these bounds, making these bounds sharp. There are additional algorithms for finding vertex-magic labelings for cycle graphs with an odd number of vertices.