My research lies in the branch of mathematics called combinatorics. More specifically, I study graph theory and network science. The main topics of my research are explained below along with links to some of my papers.
I worked with Qinghong Zhang, Alyssa Cherry, and Linda Lawton while at NMU to count the number of round-robin tournaments generated from the "standard algorithm" and showed that this algorithm does not generate all possible tournaments. This article was first published in Elemente der Mathematik in Volume 71 (2016) published by the European Mathematical Society: Counting Round-Robin Tournament Schedules © 2016 EMS Press
My doctoral thesis is titled Variations in Ramsey Theory. In this work, I provide an overview of the subject and explore variations on the classical Ramsey numbers. The activity Ramsey's Realm on my Blog page introduces the participant to the classical Ramsey numbers.
The entirety of my dissertation can be found here through ScholarWorks @ WMU: Variations in Ramsey Theory
We define this concept, introduce graph ideals, and find the down arrow Ramsey set of cycles, paths, and complete graphs up to order 7 in the paper found here: MCCCC Volume 117
You can find a visualizer and python code to generate graph ideals and the down arrow set of graph on my GitHub.
I worked with Gary Chartrand, Nazreen Almohanna, and Ping Zhang at Western Michigan University to produce two papers. Nazreen would also go on to write her dissertation on the subject. I later worked on this project at Purdue University Fort Wayne with Robert "Chip" Vandell.
You can find python code to generate the uniform spectrum of a given graph on my GitHub.