Date of Award
Spring 2023
Degree Type
Thesis
Department
Mathematics
Director of Thesis
Joshua Cooper
First Reader
Michael Filaseta
Second Reader
Michael Filaseta
Abstract
This thesis begins with a selective overview of problems in geometric graph theory, a rapidly evolving subfield of discrete mathematics. We then narrow our focus to the study of unit-distance graphs, Euclidean coloring problems, rigidity theory and the interplay among these topics. After expounding on the limitations we face when attempting to characterize finite, separable edge-maximal unit-distance graphs, we engage an interesting Diophantine problem arising in this endeavor. Finally, we present a novel subclass of finite, separable edge-maximal unit distance graphs obtained as part of the author's undergraduate research experience.
First Page
1
Last Page
69
Recommended Citation
Weatherspoon, Kaylee, "Structure of Extremal Unit Distance Graphs" (2023). Senior Theses. 616.
https://scholarcommons.sc.edu/senior_theses/616
Rights
© 2023, Kaylee Weatherspoon
