The Pi-Pebbling Function

T. Ballie Arnold

The Pi-Pebbling Function

Combinatorics 2007-05-23 v1

Authors: T. Ballie Arnold

Abstract

Recent research in graph pebbling has introduced the notion of a cover pebbling number. Along this same idea, we develop a more general pebbling function Pi(G, t, P). This measures the minimum number of pebbles needed to guarantee that any distribution of them on G can be transformed via pebbling moves to a distribution with pebbles on t target vertices. Furthermore, the P part of the function gives the ability to change how many pebbles are needed to pebble from one vertex to another. Bounds on the Pi-pebbling function are developed, as well as its exact value for several families of graphs.

Keywords

graph pebbling

Cite

@article{arxiv.math/0506438,
  title  = {The Pi-Pebbling Function},
  author = {T. Ballie Arnold},
  journal= {arXiv preprint arXiv:math/0506438},
  year   = {2007}
}