Optimal pebbling of paths and cycles

Details Optimal pebbling of paths and cycles Optimal pebbling of paths and cycles

2005-06-03

arxiv.org/abs/math/0506076v1

Mathematics

Combinatorics

8 pages; submitted to Discrete Mathematics (Fall, 2003)

Scientific paper

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.

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