Trampoline Graphs and Estimates of Their Pebbling Numbers

Abstract

Graph pebbling is a mathematical game in which pebbles are placed on the vertices of a graph. The game is made up of a series of pebbling steps that consist of removing two pebbles from one vertex, discarding a pebble, and placing the other on an adjacent vertex. The goal of the game is to reach a particular vertex by performing a series of pebbling steps. This paper will focus on implementing particular pebbling strategies on specific types of graphs to determine the minimum amount of pebbles needed to reach a vertex via pebbling moves. We will use these strategies as a basis for determining the lower bound of the pebbling number of our graph.