The t -pebbling number of squares of cycles

Abstract

Let CC be a configuration of pebbles on a graph GG. A pebbling move (step) consists of removing two pebbles from one vertex, throwing one pebble away, and moving the other pebble to an adjacent vertex. The tt-pebbling number, ft(G)ft(G), of a connected graph GG, is the smallest positive integer such that from every configuration of ft(G)ft(G) pebbles, t pebbles can be moved to any specified target vertex by a sequence of pebbling moves. In this paper, we determine the t-pebbling number for squares of cycles.