Optimal Pebbling in Products of Graphs

Details Optimal Pebbling in Products of Graphs Optimal Pebbling in Products of Graphs

2009-07-31

arxiv.org/abs/0907.5577v1

Mathematics

Combinatorics

28 pages, 1 figure

Scientific paper

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 $C_5$. Finally, we present explicit distributions which provide asymptotic bounds on optimal pebbling numbers of hypercubes.

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