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arXiv · 1411.0923

The Optimal Rubbling Number of Ladders, Prisms and M\"obius-ladders

Gyula Y. Katona·László F. Papp
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Abstract

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 $m$ 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 M\"oblus-ladders.

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Gyula Y. Katona, László F. Papp. 2014-11-04. The Optimal Rubbling Number of Ladders, Prisms and M\"obius-ladders. https://doi.org/10.1016/j.dam.2015.10.026

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