  Distributions of pebbles to the vertices of a graph are said to be solvable
when a pebble may be moved to any specified vertex using a sequence of
admissible pebbling rules. The optimal pebbling number is the least number of
pebbles needed to create a solvable distribution. We provide a simpler proof
verifying Pachter, Snevily and Voxman's determination of the optimal pebbling
number of paths, and then adapt the ideas in this proof to establish the
optimal pebbling number of cycles. Finally, we prove the optimal-pebbling
version of Graham's conjecture.
