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.