# Bounds on the Rubbling and Optimal Rubbling Numbers of Graphs

Gyula Y. Katona, Nandor Sieben

Research output: Contribution to journalArticle

2 Citations (Scopus)

### 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 rubbling number 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 give bounds for rubbling and optimal rubbling numbers.

Original language English (US) 487-492 6 Electronic Notes in Discrete Mathematics 38 https://doi.org/10.1016/j.endm.2011.09.079 Published - Dec 1 2011

### Fingerprint

Graph in graph theory
Vertex of a graph

### Keywords

• Bounded diameter
• Pebbling
• Rubbling

### ASJC Scopus subject areas

• Discrete Mathematics and Combinatorics
• Applied Mathematics

### Cite this

In: Electronic Notes in Discrete Mathematics, Vol. 38, 01.12.2011, p. 487-492.

Research output: Contribution to journalArticle

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