Date of Award

January 2018

Degree Type

Open Access Thesis

Document Type

Master Thesis

Degree Name

Master of Science (MS)

Department

Mathematics and Statistics

First Advisor

Rachel Bishop-Ross

Department Affiliation

Mathematics and Statistics

Second Advisor

Donald Jason Gibson

Department Affiliation

Mathematics and Statistics

Third Advisor

Bangteng Xu

Department Affiliation

Mathematics and Statistics

Abstract

In this paper, we will contribute to research on a Graph Theory problem known as the Gold Grabbing Game. The game consists of two players and a tree in which each vertex has a positive integer value of gold. Players take turns removing leaves from the tree and deleting the associated edge until the graph is entirely empty. A winning condition is acquiring at least half of the total gold. Existing research shows that for a tree with an even number of vertices, Player 1 can always win.

It can also be shown via simple examples that for a tree with an odd number of vertices, the game board may favor Player 1 or Player 2, depending on the conguration of the tree, the integer values at a given vertex, or both. We will expand on the reason for Player 1's advantage on even trees and attempt to clarify the winning strategy, while also expanding on the case of an odd tree and various winning scenarios for Player 1 or 2.

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