Conditions for Weighted Cover Pebbling of Graphs

Details Conditions for Weighted Cover Pebbling of Graphs Conditions for Weighted Cover Pebbling of Graphs

2004-10-18

arxiv.org/abs/math/0410410v1

Mathematics

Combinatorics

8 pages

Scientific paper

In a graph G with a distribution of pebbles on its vertices, a pebbling move is the removal of two pebbles from one vertex and the addition of one pebble to an adjacent vertex. A weight function on G is a non-negative integer-valued function on the vertices of G. A distribution of pebbles on G covers a weight function if there exists a sequence of pebbling moves that gives a new distribution in which every vertex has at least as many pebbles as its weight. In this paper we give some necessary and some sufficient conditions for a distribution of pebbles to cover a given weight function on a connected graph G. As a corollary, we give a simple formulation for the `weighted cover pebbling number' of a weight function W and a connected graph G, defined by Crull et al. to be the smallest number m such that any distribution on G of m pebbles is a cover for W. Also, we prove a cover pebbling variant of Graham's Conjecture for pebbling.

Affiliated with

Also associated with

No associations

Rating

Conditions for Weighted Cover Pebbling of 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 Conditions for Weighted Cover Pebbling of Graphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Conditions for Weighted Cover Pebbling of Graphs will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-513460