Optimal pebbling of graphs

AbstractConsider a distribution of pebbles on the vertices of a graph G. A pebbling move consists of the removal of two pebbles from a vertex and then placing one pebble at an adjacent vertex. The optimal pebbling number of G, denoted fopt(G), is the least number of pebbles, such that for some distribution of fopt(G) pebbles, a pebble can be moved to any vertex of G.We give sharp lower and upper bounds for fopt(G) for G of diameter d. For graphs of diameter two (respectively, three) we characterize the classes of graphs having fopt(G) equal to a value between 2 and 4 (respectively, between 3 and 8)