Critical Pebbling Numbers of Graphs

Authors

Courtney R. Gibbons, Hamilton CollegeFollow
Joshua D. Laison
Erick J. Paul

Type of Work

Article

Date

2016

Journal Title

Journal of Combinatorial Mathematics and Combinatorial Computing

Journal ISSN

0835-3026

Journal Volume

99

First Page

199

Last Page

224

Abstract

We define three new pebbling parameters of a connected graph G, the r-, g-, and u-critical pebbling numbers. Together with the pebbling number, the optimal pebbling number, the number of vertices n and the diameter d of the graph, this yields 7 graph parameters. We determine the relationships between these parameters. We investigate properties of the r-critical pebbling number, and distinguish between greedy graphs, thrifty graphs, and graphs for which the r-critical pebbling number is 2d.

Citation Information

Gibbons, Courtney R.; Laison, Joshua D.; and Paul, Erick J., "Critical Pebbling Numbers of Graphs" (2016). Hamilton Digital Commons.
https://digitalcommons.hamilton.edu/articles/272

Notes

This page links to a version of the paper posted at arXiv.org on January 17, 2015.

The article was published in: Journal of Combinatorial Mathematics and Combinatorial Computing, vol. 99 (2016): 199-224.

Hamilton Areas of Study

Mathematics