Author ORCID Identifier
Date Available
7-27-2023
Year of Publication
2023
Degree Name
Doctor of Philosophy (PhD)
Document Type
Doctoral Dissertation
College
Arts and Sciences
Department/School/Program
Mathematics
First Advisor
Dave Jensen
Abstract
Chip firing is a category of games played on graphs. The gonality of a graph tells us how many chips are needed to win one variation of the chip firing game. The focus of this dissertation is to provide a variety of new strategies to compute the gonality of various graph families. One family of graphs which this dissertation is particularly interested in is rook graphs. Rook graphs are the Cartesian product of two or more complete graphs and we prove that the gonality of two dimensional rook graphs is the expected value of (n − 1)m where n is the size of the smaller complete graph and m is the size of the larger.
Digital Object Identifier (DOI)
https://doi.org/10.13023/etd.2023.310
Recommended Citation
Speeter, Noah, "Methods of Computing Graph Gonalities" (2023). Theses and Dissertations--Mathematics. 104.
https://uknowledge.uky.edu/math_etds/104
