The optimal rubbling number of ladders, prisms and Mobius-ladders

A pebbling move on a graph removes two pebbles at a vertex and adds one pebble at an adjacent vertex. Rubbling is a version of pebbling where an additional move is allowed. In this new move, one pebble each is removed at vertices v and w adjacent to a vertex u, and an extra pebble is added at vertex u. A vertex is reachable from a pebble distribution if it is possible to move a pebble to that vertex using rubbling moves. The optimal rubbling number is the smallest number m needed to guarantee a pebble distribution of in pebbles from which any vertex is reachable. We determine the optimal rubbling number of ladders (P-n square P-2), prisms (C-n square P-2) and Mobius-ladders. (C) 2015 Elsevier B.V. All rights reserved.