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.