Vertex-Magic Graphs

In graph theory, a graph labeling is an assignment of labels to the edges and vertices of a graph. There are many different types of graphs labelings. Some include graceful labelings, harmonious labelings, and magic labelings. In this project we will focus on a type of magic labeling. A vertex-magic total labeling is a labeling such that the vertices and edges are assigned consecutive integers between 1 and v+e, where v is the order of the graph and e is the size of the graph. When the sum of the labels of a vertex and its incident edges results in the same integer for each vertex, we have a vertex-magic total labeling. This integer is called the magic number of the graph and the graph is called a vertex-magic graph. There has been previous research on vertex-magic total labelings and we know a lot about certain classes of graphs. In this project, we are considering crown graphs. We will give upper and lower bounds of the magic number, a function that generates vertex-magic total labelings of crown graphs and discuss other results about this kind of labeling