The Optimal Pebbling Number of Square of Paths and Cycles

Abstract

A pebbling move involves removing two pebbles from one vertex and placing one on an adjacent vertex. The optimal pebbling number of a graph $G$, denoted by $f_{opt}(G)$, is the least positive integer $n$ such that $n$ pebbles are placed suitably on vertices of $G$ and, for any specified vertex $v$ of $G$, one pebble can be moved to $v$ through a sequence of pebbling moves. In this paper, we determine the optimal pebbling number of the square of paths and cycles.