THE OPTIMAL PEBBLING NUMBER OF THE CATERPILLAR

Abstract

Let G be a simple graph. If we place p pebbles on the vertices of G, then a pebbling move is taking two pebbles off one vertex and then placing one on an adjacent vertex. The optimal pebbling number of G, f'(G), is the least positive integer p such that p pebbles are placed suitably on vertices of G and for any target vertex nu of G, we can move one pebble to nu by a sequence of pebbling moves. In this paper, we find the optimal pebbling number of the caterpillars.