The $t$-Pebbling Number and $2t$-Pebbling Property on the Graph $D_{n,C_{2m}}$

Abstract

Given a distribution $D$ of pebbles on the vertices of a graph $G$, a pebbling move on $G$ consists of removing two pebbles from a vertex and placing one on an adjacent vertex (the other is discarded). The pebbling number of $G$, denoted $f(G)$, is the smallest integer $k$ such that any distribution of $k$ pebbles on $G$ allows one pebble to be moved to any specified vertex via pebbling moves. In this paper, we calculate the $t$-pebbling number of the graph $D_{n,C_{2m}}$. Furthermore, we verify the $q$-$t$-pebbling number to demonstrate that $D_{n,C_{2m}}$ possesses the $2t$-pebbling property.