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The pebbling number of C5 × C5

✍ Scribed by David S. Herscovici; Aparna W. Higgins

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
519 KB
Volume
187
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

✦ Synopsis

Chung has defined a pebbling move on a graph G to be the removal of two pebbles from one vertex and the addition of one pebble to an adjacent vertex. The pebbling number f(G) of a connected graph is the least number of pebbles such that any distribution of f(G) pebbles on G allows one pebble to be moved to any specified, but arbitrary vertex. Graham conjectured that for any connected graphs G and H, f(G x H)<<, f(G)f(H). We show that Graham's conjecture holds when G=H = C5.

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