Pebbling is a game played on a graph. In a pebbling step, two
pebbles can be removed from one vertex, and one of them is replaced on
an adjacent vertex. This program can be used to create interesting
pebbling configurations on graphs. One such a problem is related to so
called non-greedy pebbling described below.
The graph on the picture has a non-greedy configuration: to get
root vertex (R) you need to move away from it first. This configuration
8 pebbles and the pebbling number of the graph is 9. Can you find a
with non-greedy configuration that has as many pebbles as its pebbling
More info on pebbling can also be found at http://mingus.la.asu.edu/~hurlbert/pebbling/pebb.html.
Pebbling Applet Description:In this program, you can create a graph,
place pebbles on the vertices, and make pebbling moves.
New version of the pebbling applet is available at pebbleit.hope.edu.
There are two
versions of the program:
FULL VERSION EXCLUSIVE FEATURES - File Saving/Loading
full version there is a special dropdown menu available at the top of
the screen that allows you to save and load the graph.
Save - This will save your graph and pebbling configuration
Save graph only - This will save your blank graph
Load - This will load any graph you have saved
WHY FULL/BASIC VERSIONS?
The full version requires you to accept a security certificate; this
is so the java applet has the ability to read/write files on your
computer. The source code is available on the main page if you wish to
inspect exactly what this program is doing. If you do not feel safe
running the Full Version, there is a Basic Version that removes the
ability to Save and Load graphs.
Note: Both versions of the applet require Java 1.4.2_08 or
higher. Free download and more details you can find at their website.
All source files can be
freely distributed and modified under GNU General
Public License. In order to access files you need WinZip or any other compatible
If you have any questions this guide has not addressed, suggestions
for this program, or have found bugs in the program, send an email to
Airat Bekmetjev at firstname.lastname@example.org.