Herscovici's conjecture on C2n x G

The t-pebbling number, f(t)(G), of a connected graph C, is the smallest positive integer such that from every placement of f(t)(G) pebbles, t pebbles can be moved to any specified target vertex by a sequence of pebbling moves, each move taking two pebbles off a vertex and placing one on an adjacent vertex. A graph G satisfies the 2t-pebbling property if 2t pebbles can be moved to any specified vertex when the total starting number of pebbles is 2f(t)(G) - q + 1, where q is the number of vertices with at least one pebble. We show that the cycle C-2n satisfies the 2t-pebbling property. Herscovici conjectured that for any connected graphs G and H, f(st)(G x H) <= f(s )(G) f(t) (H). We prove Herscovici's conjecture is true, when G is an even cycle and for variety of graphs H which satisfy the 2t-pebbling property.