66 research outputs found
Optimal Pebbling in Products of Graphs
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 -pebbling
numbers for specific such products. We obtain bounds on optimal pebbling
numbers of powers of the cycle . Finally, we present explicit
distributions which provide asymptotic bounds on optimal pebbling numbers of
hypercubes.Comment: 28 pages, 1 figur
Cover Pebbling Hypercubes
Given a graph G and a configuration C of pebbles on the vertices of G, a
pebbling step removes two pebbles from one vertex and places one pebble on an
adjacent vertex. The cover pebbling number g=g(G) is the minimum number so that
every configuration of g pebbles has the property that, after some sequence of
pebbling steps, every vertex has a pebble on it. We prove that the cover
pebbling number of the d-dimensional hypercube Q^d equals 3^d.Comment: 11 page
- …