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 $v$ 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 caterpillars.