  A pebbling move on a weighted graph removes some pebbles at a vertex and adds
one pebble at an adjacent vertex. The number of pebbles removed is the weight
of the edge connecting the vertices. A vertex is reachable from a pebble
distribution if it is possible to move a pebble to that vertex using pebbling
moves. The pebbling number of a weighted graph is the smallest number $m$
needed to guarantee that any vertex is reachable from any pebble distribution
of $m$ pebbles. Regular pebbling problems on unweighted graphs are special
cases when the weight on every edge is 2. A regular pebbling problem often
simplifies to a pebbling problem on a simpler weighted graph. We present an
algorithm to find the pebbling number of weighted graphs. We use this algorithm
together with graph simplifications to find the regular pebbling number of all
connected graphs with at most nine vertices.
