Define a pebbling move as a transer of two pebbles from one vertex of a graph edge to an adjacent vertex with one of the pebbles being removed in transit as a toll.
The pebbling number
of a graph
is the smallest
such that every supply of pebbles can satisfy every demand of one pebble (Hurlbert 2011).
Computing the pebbling number is NP-complete
(Hurlbert 2011).

The values of the pebbling number for various classes of graphs are given in the table below (Hurlbert).

Chung, F. R. K. "'Pebbling in Hypercubes." SIAM J. Disc. Math.2, 467-472, 1989.Hurlbert, G. "A
Linear Optimization Technique for Graph Pebbling." 28 Jan 2011. https://arxiv.org/abs/1101.5641.Hurlbert,
G. "General Graph Pebbling." Disc. Appl. Math.161, 1221-1231,
2013.Hurlbert, G. "Graph Pebbling Numbers Page." http://www.people.vcu.edu/~ghurlbert/pebbling/pnummain.html.Milans,
K. and Clark, B. "The Complexity of Graph Pebbling." SIAM J. Disc. Math.20,
769-798, 2006.