A graph pebbling algorithm on weighted graphs

Details A graph pebbling algorithm on weighted graphs A graph pebbling algorithm on weighted graphs

2009-04-10

arxiv.org/abs/0904.1651v1

Mathematics

Combinatorics

Scientific paper

A pebbling move on a weighted graph removes some pebbles at a vertex and adds one pebble at an adjacent vertex. The number of pebbles removed is the weight of the edge connecting the vertices. A vertex is reachable from a pebble distribution if it is possible to move a pebble to that vertex using pebbling moves. The pebbling number of a weighted graph is the smallest number $m$ needed to guarantee that any vertex is reachable from any pebble distribution of $m$ pebbles. Regular pebbling problems on unweighted graphs are special cases when the weight on every edge is 2. A regular pebbling problem often simplifies to a pebbling problem on a simpler weighted graph. We present an algorithm to find the pebbling number of weighted graphs. We use this algorithm together with graph simplifications to find the regular pebbling number of all connected graphs with at most nine vertices.

Affiliated with

Also associated with

No associations

Rating

A graph pebbling algorithm on weighted graphs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A graph pebbling algorithm on weighted graphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A graph pebbling algorithm on weighted graphs will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-673809