A graph 
has the 2-pebbling property if, for any distribution of more
than 
pebbles on 
,
where 
is the pebbling number and 
is the number of vertices receiving at least one pebble in
the distribution, it is possible to move two pebbles to any specified target vertex
using pebbling moves.
The 2-pebbling property is a strengthening related to graph pebbling and the pebbling number. The Lemke graph is the smallest graph that does not have the 2-pebbling property (Hurlbert 2013).
