The cover pebbling number of graphs

A pebbling move on a graph consists of taking two pebbles off of one vertex and placing one pebble on an adjacent vertex. In the traditional pebbling problem we try to reach a specified vertex of the graph by a sequence of pebbling moves. In this paper we investigate the case when every vertex of the graph must end up with at least one pebble after a series of pebbling moves. The cover pebbling number of a graph is the minimum number of pebbles such that however the pebbles are initially placed on the vertices of the graph we can eventually put a Department of Mathematics and Computer Science, Valparaiso University, Valparaiso, Indiana 46383-6493. Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287-1804. email: [email protected]. Partially supported by National Security Agency grant #MDA9040210095. Department of Mathematics and Computer Science, Valparaiso University, Valparaiso, Indiana 46383-6493. email: [email protected]. Computer and Automation Institute of the Hungarian Academy of Sciences, Budapest; and Department of Computer Science, University of Veszprém, Hungary. Partially supported by OTKA grant T-032969.