student projects
John Caughman, 2024

Name Degree Year Project Title

Benim, Robert

MS

2010

Enumerating Cyclic Quasiplatonic Groups For a Given Signature (slides)

Benjamin, Brad

MS

2007

The Algebra of the 2x2x2 Rubik’s Cube

Bourke, Haley

MS

2022

Optimal Integer Visibility Bar Graphs of Trees

Bracher, Kylee

MS

2005

The Law of Quadratic Reciprocity: Proof by Wilson's Theorem

Bushi, Jaime

MS

2012

Optimal Strategies for Hat Games (slides)

Calmer, Brenna

MS

2020

Geometric Graph Homomorphisms and the Geochromatic Number

Carter, Brittany

MS

2018

Proving Eulerian triangulations are 3-colorable (slides)

Casey, Levi

MS

2017

Reidemeister-Schreier Rewriting Process for Group Presentations (slides)

Chura, Nickolas

MS

2007

Alternating Sign Matrices and Symmetry (slides)

Cottrell, Ross

MST

2006

Limits, Sequences, and Series

Daleson, Gabriel

MS

2006

Deterministic Primality Testing in Polynomial Time

De Grasse, Charles

MS

2007

Weighted Forms of Euler's Theorem

DeHoff, Emily

Sr proj.

2022

Minimality of Integer Bar Visibility Graphs

Denny, Natalie

MS

2020

Bounds on the Largest Eigenvalue of the Distance Matrix (slides)

Dunaway, Michelle

MS

2020

Generalizing Vizing's Theorem to Multigraphs

Enkhjargal, Minjin

Sr proj.

2021

Spanning Trees of Complete Graphs and Cycles

Erickson, Ander

MS

2007

Representing Permutations with Tableaux

Flowerday, Kaelyn

Sr proj.

2015

Unfolding Trees and Symmetrically-Associated Graphs

Gildersleeve, Nate

MST

2013

The Gossip Problem (slides)

Haithcock, Cliff

MS

2005

Hamiltonicity and Fault Tolerance in the k-ary n-cube

Han, Simon Byeonguk

MS

2022

The Fox Calculus and Differentiation in Group Rings

Herman, Ari

MS

2019

Distances, Diameter, Girth and Odd Girth in Generalized Johnson Graphs

Herman, Ari

PhD

2024

Tree Width and Density of Generalized Johnson Graphs

Hochnadel, Damon

MS

2013

Cycles, Chords, and Planarity in Graphs (slides)

Hoffman, Melanie

MS

2017

Two-Toned Tilings and Compositions of Integers

Jacobs, Tony

MS

2006

Fractional Colorings and the Mycielski Graphs

Jung, Eunsuk

MS

2020

A New Lower Bound on the Chromatic Number of a Graph

Kaskowitz, Louis

MS

2006

The Independence Fractal of a Graph

Kawasaki, Tomohiro

MS

2011

Sharp Upper Bounds for the Largest Laplacian Eigenvalue of a Tree (slides)

Keller, Bryn

MS

2022

Treewidth of the Kneser Graph

Kummel, Ewan

MS

2012

Linear Extensions of LYM Posets (slides)

Kummel, Ewan

PhD

2023

Forest Generating Functions of Directed Graphs

Kuoha, Jaylin

MS

2022

A Bound for the Diameter of a Distance-regular Graph

Langford, Wil

MS

2013

On the Extremal Cases of the Identifying Code Problem

Lazar, Nathan

MS

2007

Destroying Automorphisms in Trees

Leonard, Katie

MS

2005

The Friendship Theorem and Projective Planes

Lockwood, Elise

MST

2006

The Combinatorics and Pedagogy of Matchings and Rook Polynomials

Lopresti, Shelley

MST

2006

Desargues' Theorem and the Mathematics of Perspective

Mahoney, James

PhD

2016

Tree Graphs and Orthogonal Spanning Tree Decompositions (slides)

Masuda, Shuichi

PhD

2024

Doubly Almost Bipartite Leonard Pairs

McKinley, Sky

MS

2003

The Hamming Codes and Delsarte’s Linear Programming Bound

Meagher, Tim

MS

2010

Multi-coloring and Mycielski's construction

Moore, LeKisha

MSMT

2022

From a History of Math in Games to a Future of Games in Math

Oddson, Kyle

Sr proj.

2016

Partial chromatic polynomials and Sudoku

Oddson, Kyle

MS

2019

Counting and Coloring Sudoku Graphs

Parkinson, Troy

MS

2009

The Golden Root of Chromatic Polynomials (slides)

Richards, Joe

MS

2011

Graphic Realizations of Sequences (slides)

Ridge, Matthew

MS

2013

On (Kq;k)-Stable Graphs (slides)

Rock, Katherine

MS

2016

Properties of the Towers of Hanoi Graphs (slides)

Roidt, Tom

MST

2011

Cycloids and Paths (slides)

Ross, Rebecca

MS

2007

An Infeasible Distance-regular Graph

Samuels, Kevin

Sr proj.

2009

A Dynamic Survey of Cages

Schimanski, Nichole

MS

2011

Fractional Colorings and Zykov Products of Graphs (slides)

Schimanski, Nichole

PhD

2016

Orthomorphisms of Boolean Groups

Schneider, Cynthia

MST

2011

De Moivre’s Theorem – Roots, Powers, and Complex Numbers

Smith, Cliff

MST

2010

Fibonacci Solitaire and Its Use in the Classroom (slides)

Smoyer, Laura

MST

2005

Musical Mathematics: The Mathematics of Equal Temperament

Spindel, Aaron

MS

2012

Hypergraphs With a Unique Perfect Matching (slides)

Stauth, Gabriel

MS

2017

Coherent Configurations and the Graph Isomorphism Problem

Swinyard, Craig

MST

2002

An Introductory Graph Theory Curriculum

Taylor, Joanna

MST

2005

Polynomial Multiplication and the Role of Variables

Terada, Taiyo

MS

2017

Computing Total Dominator Chromatic Numbers of Some Graphs

Terada, Taiyo

PhD

2024

Some Hypergeometric Identities and Related Leonard Pairs

Tillia, Valerie

MS

2010

Determinants of Distance Matrices of Trees (slides)

Titcomb, Kalei

MST

2009

The Problem of the 36 Officers (slides)

Vaughn, Dan

MS

2014

Rainbow Connection Numbers in Graphs

Vollet, Carly

MS

2007

The Structure of Maximum Independent Sets in Fullerenes

Walker, Ian

MST

2011

Explorations in Recursion with John Pell and the Pell Sequence

Wallulis, Karl

MS

2017

Finding Nice Permutation Polynomials over Finite Fields

Welke, Shelley

MS

2012

Electrical Resistances in Products of Graphs

Whinston, Amy

MST

2009

A Finite History of Infinity

Wolff, Nadine

MS

2001

Spin Models and Bose-Mesner Algebras

Wood, David

MSMT

2022

Integer Partitions

Wyse, Ian

MS

2020

On the Connectivity of Connected Bipartite Graphs With Two Orbits

Zhao, Richard

MSMT

2022

Josephus Permutations



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