Graham's pebbling conjecture on product of thorn graphs of complete graphs

The pebbling number of a graph G, f(G), is the least n such that, no matter how n pebbles are placed on the vertices of G, we can move a pebble to any vertex by a sequence of pebbling moves, each move taking two pebbles off one vertex and placing one on an adjacent vertex. Let p"1,p"2,...,p"n be positive integers and G be such a graph, V(G)=n. The thorn graph of the graph G, with parameters p"1,p"2,...,p"n, is obtained by attaching p"i new vertices of degree 1 to the vertex u"i of the graph G, i=1,2,...,n. Graham conjectured that for any connected graphs G and H, f(GxH)@?f(G)f(H). We show that Graham's conjecture holds true for a thorn graph of the complete graph with every p"i>1(i=1,2,...,n) by a graph with the two-pebbling property. As a corollary, Graham's conjecture holds when G and H are the thorn graphs of the complete graphs with every p"i>1(i=1,2,...,n).