Author ORCID Identifier

Date Available


Year of Publication


Degree Name

Doctor of Philosophy (PhD)

Document Type

Doctoral Dissertation


Arts and Sciences



First Advisor

Dave Jensen


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)