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Achievable Pebbling Numbers

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Aparna Higgins, University of Dayton

What
  • Graph Theory Seminar
  • Colloquium
When Fri, Apr 24, 2009
from 11:00 AM to 11:50 AM
Where RH 316
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Given a connected graph G and a distribution of non-negative integers on its vertices, a pebbling move on G is defined as the removal of two pebbles from one vertex, followed by the placement of one of those pebbles on an adjacent vertex.  The pebbling number f(G) of a graph is the minimum number of pebbles needed such that, given any distribution of f(G) pebbles on G, one pebble can be placed on any specified but arbitrary vertex through a sequence of pebbling moves.  It is known that for a graph G with n vertices, n ≤ f(G) ≤ 2^(n-1).  In this talk, I will describe our attempts to determine which of the integers in the interval [n, 2^(n-1) ] can be realized as the pebbling number of a graph on n vertices.   

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