Abstract: Consider a connected graph with pebbles distributed on its vertices. A pebbling move on such a graph consists of removing two pebbles from any one vertex, discarding one of those pebbles and moving the other pebble to an adjacent vertex. The pebbling number of a graph is defined as the least number of pebbles m, such that, for any distribution of m pebbles, one pebble can be moved to any designated vertex using a sequence of pebbling moves. In the fifteen years since the pebbling number of a graph was defined, undergraduates around the country have contributed significantly to the body of results on pebbling. Their results have been published in research journals and have been presented (with contagious excitement!) in contributed talks and in poster sessions. This talk will focus on some undergraduate pebblers and their results.

This talk was originally given by Aparna Higgins as an MAA Invited Address at the Providence MathFest in August 2004.