Rubbling and Optimal Rubbling of Graphs
| dc.creator | Belford, Christopher | |
| dc.creator | Sieben, Nandor | |
| dc.date | 2007-07-28 | |
| dc.date.accessioned | 2026-07-07T08:20:55Z | |
| dc.date.available | 2026-07-07T08:20:55Z | |
| dc.description | 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 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 rubbling number of a graph is the smallest number m needed to guarantee that any vertex is reachable from any pebble distribution of m pebbles. 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 rubbling and optimal rubbling number of some families of graphs including cycles. | |
| dc.description | 14 pages | |
| dc.identifier | https://arxiv.org/abs/0707.4256 | |
| dc.identifier | http://arxiv.org/abs/0707.4256 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/135207 | |
| dc.subject | Combinatorics | |
| dc.title | Rubbling and Optimal Rubbling of Graphs | |
| dc.type | text |