Mathematics – Combinatorics
Scientific paper
2004-10-06
Mathematics
Combinatorics
5 pages
Scientific paper
For any configuration of pebbles on the nodes of a graph, a pebbling move replaces two pebbles on one node by one pebble on an adjacent node. A cover pebbling is a move sequence ending with no empty nodes. The number of pebbles needed for a cover pebbling starting with all pebbles on one node is trivial to compute and it was conjectured that the maximum of these simple cover pebbling numbers is indeed the general cover pebbling number of the graph. That is, for any configuration of this size, there exists a cover pebbling. In this note, we prove a generalization of the conjecture. All previously published results about cover pebbling numbers for special graphs (trees, hypercubes etcetera) are direct consequences of this theorem. We also prove that the cover pebbling number of a product of two graphs equals the product of the cover pebbling numbers of the graphs.
No associations
LandOfFree
The cover pebbling theorem 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 The cover pebbling theorem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The cover pebbling theorem will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-171057