2-target pebbling number of graphs

Chung defined the pebbling move of a graph which involves choosing a vertex with at least two pebbles, discarding those two pebbles from that vertex and adding one pebble to a nearby vertex. The 2-target pebbling number of the vertices u,v in graph a G is the least number φ(G,u,v) has the characteristic that for every configuration of φ(G,u,v) pebbles on G, it is possible to move a pebble to u and v simultaneously by a sequence of pebbling moves. The 2-target pebbling number of graph G, denoted by φ(G), is the maximum φ(G,u,v) over all pairs of the vertices in G. In this paper, we discuss the 2-target pebbling number for some standard graphs.