The Optimal Pebbling Number of the Caterpillar

Let G be a simple graph. If we place p pebbles on the vertices of G, then a pebbling move is taking two pebbles o one vertex and then placing one on an adjacent vertex. The optimal pebbling number of G, f0(G), is the least positive integer p such that p pebbles are placed suitably on vertices of G and for any target vertex v of G, we can move one pebble to v by a sequence of pebbling moves. In this paper, we find the optimal pebbling number of the caterpillar. Key word. Optimal pebbling, Caterpillar. AMS(MOS) subject classification. 05C05