We prove a generalization of Graham's Conjecture for optimal pebbling with
arbitrary sets of target distributions. We provide bounds on optimal pebbling
numbers of products of complete graphs and explicitly find optimal t-pebbling
numbers for specific such products. We obtain bounds on optimal pebbling
numbers of powers of the cycle C5​. Finally, we present explicit
distributions which provide asymptotic bounds on optimal pebbling numbers of
hypercubes.Comment: 28 pages, 1 figur