9 papers
The -gonal locus in the moduli space of tropical plane curves
Desmond Leitz, Ralph Morrison, Søren Newman-Taylor +1
We introduce and study the locus of genus tropical plane curves of gonality inside the moduli space of tropica…
Chip-Firing Games on Banana Trees
Marchelle Beougher, Nila Cibu, Kexin Ding +6
We study chip-firing games on multigraphs whose underlying simple graphs are trees, paths, and stars, denoted as banana trees, paths, and stars respectively. We present a polynomia…
The tropical crossing number of a finite graph
Noah Cape, Ralph Morrison
In 2015, Cartwright et al. showed that any -regular metric graph arises as the skeleton of a tropical plane curve with nodes allowed. They introduced the tropical crossing numbe…
The gonality of circulant graphs
Lisa Cenek, Lizzie Ferguson, Eyobel Gebre +5
The gonality of a graph measures how difficult it is to move chips around the entirety of a graph according to certain chip-firing rules without introducing debt. In this paper we…
Commuting graphs of -adic matrices
Ralph Morrison
We study the commuting graph of matrices over the field of -adics , whose vertices are non-scalar matrices with entries in a…
Chip-firing on the Platonic solids: a primer for studying graph gonality
Marchelle Beougher, Kexin Ding, Max Everett +4
This paper provides a friendly introduction to chip-firing games and graph gonality. We use graphs coming from the five Platonic solids to illustrate different tools and techniques…
The gonality of chess graphs
Nila Cibu, Kexin Ding, Steven DiSilvio +4
Chess graphs encode the moves that a particular chess piece can make on an chessboard. We study through these graphs through the lens of chip-firing games and graph gon…
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…
On the size and complexity of scrambles
Seamus Connor, Steven DiSilvio, Sasha Kononova +2
The scramble number of a graph, a natural generalization of bramble number, is an invariant recently developed to study chip-firing games and graph gonality. We introduce the carto…