Project Description
Graph pebbling consists of placing "pebbles" or markers on vertices of a simple graph and moving the pebbles according to the following rule: There must be at least two pebbles on a given vertex in order to make a pebbling move. A pebbling move from one vertex to an adjacent vertex consists of removing one pebble from the initial vertex and moving a second pebble from the initial vertex to the terminal vertex. The pebbling number of a graph, p(G), is the minimum number of of pebbles needed to, after a series of pebbling moves, have a pebble at any given vertex, given any initial configuration of the p(G) pebbles. A class-0 graph G on n vertices is one in which p(G) = n. We define a k class-0 graph G as one in which a simple graph G can be partitioned into k class-0 subgraphs on n vertices. Previous results have shown that complete graphs on n vertices, Kn, are k class-0 for a given n > N for some integer N (Fiorini, Verbeck, de Silva). This project will explore additional questions related to pebbling and k class-0 graphs.