Graph pebbling is a model aiming to solve the following resource allocation question: can a given supply meet some predetermined demand? A pebbling move is defined as taking two pebbles from a vertex and placing one pebble on a neighboring vertex. Given a graph G, the pebbling number π(G) is the minimum number of pebbles such that any configuration of that size can satisfy the target demand through a sequence of pebbling moves.

Graph pebbling on the hypercube was originally developed by Fan Chung as an alternate proof technique to resolve the Erdos-Lemke conjecture in number  ̋ theory. Since then, the pebbling number and variations have been studied for various classes of graphs. This talk will survey existing results and techniques used to determine the pebbling number, with a focus on the hypercube. It will also explore how generalizing techniques from the hypercube connects to Graham’s conjecture and further enriches the world of graph pebbling.