A Pebbling Game on Powers of Paths

Authors

Garth Isaak, Lehigh UniversityFollow
Matthew Prudente, Alvernia UniversityFollow
Joseph M. Marcinik III, University of California, Los AngelesFollow

DOI Link

https://doi.org/10.70013/nq3t7kl0

Abstract

Two Player Graph Pebbling is an extension of graph pebbling. Players Mover and Defender use pebbling moves, the act of removing two pebbles from one vertex and placing one pebble on an adjacent vertex, to win. If a specified vertex has a pebble on it, then Mover wins. If a specified vertex is pebble-free and there are no more valid pebbling moves, then Defender wins. The Two-Player Pebbling Number of a graph G, η(G), is the minimum m such that for every arrangement of m pebbles and for any specified vertex, Mover can win. We specify the winning player for powers of a path.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Recommended Citation

Isaak, Garth; Prudente, Matthew; and Marcinik, Joseph M. III (2023) "A Pebbling Game on Powers of Paths," Communications on Number Theory and Combinatorial Theory: Vol. 4, Article 1.
DOI: 10.70013/nq3t7kl0
Available at: https://research.library.kutztown.edu/contact/vol4/iss1/1