Distance Pebbling on Directed Cycle Graphs

Abstract

Let $G$ be a graph. We define the distance $d$ pebbling number of $G$ to be the smallest number $s$ such that if $s$ pebbles are placed on the vertices of $G$, then there must exist a sequence of pebbling moves which takes a pebble to a vertex which is at a distance of at least $d$ from its starting point. In this article, we evaluate the distance $d$ pebbling numbers for a directed cycle graph with $n$ vertices.