Bounds on the Rubbling and Optimal Rubbling Numbers of Graphs

Gyula Y. Katona, Nándor Sieben

Research output: Contribution to journalArticle

2 Scopus citations

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 languageEnglish (US)
Pages (from-to)487-492
Number of pages6
JournalElectronic Notes in Discrete Mathematics
Volume38
DOIs
StatePublished - Dec 1 2011

Keywords

  • Bounded diameter
  • Pebbling
  • Rubbling

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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