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math.CO2023
The Gonality of Queen's Graphs
Ralph Morrison, Noah Speeter
In this paper we study queen's graphs, which encode the moves by a queen on an chess board, through the lens of chip-firing games. We prove that their gonality is equal…
math.CO2022
The Gonality of Rook Graphs
Noah Speeter
Two dimensional rook graphs are the Cartesian product of two complete graphs. In this paper we prove that the gonality of these graphs is the expected value of where i…
math.CO2020
A New Lower Bound on Graph Gonality
Michael Harp, Elijah Jackson, David Jensen +1
We define a new graph invariant called the scramble number. We show that the scramble number of a graph is a lower bound for the gonality and an upper bound for the treewidth. Unli…