Pebbling Number of The Graph $D_{n,C_m}$

Abstract

Given a distribution $D$ of pebbles on the vertices of a graph $G$, a pebbling move consists of removing two pebbles from a vertex and placing one on an adjacent vertex (the other is discarded). The pebbling number of a graph, denoted by $f(G)$, is the minimal integer $k$ such that any distribution of $k$ pebbles on $G$ allows one pebble to be moved to any specified vertex by a sequence of pebbling moves. In this paper, we calculate the pebbling number of the graph $D_{n,C_m}$ and consider the relationship the pebbling number between the graph $D_{n,C_m}$ and the subgraphs of $D_{n,C_m}$.