Extensions of Graph Pebbling

My thesis will consist of extensions to results that I proved at the 2004 East Tennessee State REU. Most of these results have to do with graph pebbling and various probabilistic extensions. Specifically, in Chapter 2 we compute the cover pebbling number for complete multipartite graphs and prove upper bounds for cover pebbling numbers for graphs of a specified diameter and order. We also prove that the cover pebbling decision problem is NP complete. In Chapters 3 and 4 we examine domination cover pebbling. In Chapter 5, we obtain structural and probabilistic results for deep graphs, and in Chapter 6 we compute cover pebbling probability thresholds for the complete graph