Global Properties of Some Preferential Attachment Graphs

We are looking at a model of preferential attachment graphs that can evolve in five different ways. On any given iteration, a single vertex may be connected to the graph, a path may be connected to the graph, an edge may be added to the graph, an edge may be removed from a graph, or a vertex may be removed from a graph, with each option having a given probability of occurring. If a single vertex or a path is added, one or both of the new vertices also may be connected to the neighborhood of the existing vertex. We explore the order, size, and degree distribution of the graphs which result from a large number of iterations. Acknowledgment Special thanks to Angela Collier and Blake Nickell for all of their help with this project, and to Dr. R. Duane Skaggs for being an excellent advisor.