Honors Program

University Honors

Date of Award

5-2021

Thesis Professor(s)

Robert A. Beeler

Thesis Professor Department

Mathematics and Statistics

Thesis Reader(s)

Rodney Keaton

Abstract

Peg solitaire is a game in which pegs are placed in every hole but one and the player jumps over pegs along rows or columns to remove them. Usually, the goal of the player is to leave only one peg. In a 2011 paper, this game is generalized to graphs. In this thesis, we consider a variation of peg solitaire on graphs in which pegs can be removed either by jumping them or merging them together. To motivate this, we survey some of the previous papers in the literature. We then determine the solvability of several classes of graphs including stars and double stars, caterpillars, trees of small diameter, particularly four and five, and articulated caterpillars. We conclude this thesis with several open problems related to this study.

Publisher

East Tennessee State University

Document Type

Honors Thesis - Withheld

Creative Commons License

Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.

Copyright

Copyright by the authors.

Available for download on Friday, April 15, 2022

Included in

Mathematics Commons

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