The pebbling number of C5 × C5 Original Research Article

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 × H)⩽ f(G)f(H). We show that Grahamʹs conjecture holds when G = H = C5.