Author ORCID Identifier
0000-0002-4578-5230
Defense Date
2024
Document Type
Dissertation
Degree Name
Doctor of Philosophy
Department
Systems Modeling and Analysis
First Advisor
Craig Larson
Second Advisor
Allison H. Moore
Abstract
In this thesis, we explore four projects. In the first project, we explore $r$-neighbor bootstrap percolation on a graph $G$. We establish upper bounds for the number of vertices required to percolate in the case that $r=2$ for particular classes of graphs. In the second project, we study the structure of graphs with independence number two. We prove a lower bound on the number of edges of such graphs, related to an upper bound on the number of edges in a triangle-saturated graph, and give a sufficient forbidden induced subgraph condition for independence number two graphs. In the third project, we extend an existing method and provide a robust framework for studying and analyzing the structure of RNA molecules via chord diagrams and graph theory. In the fourth project, we prove that existing graph theoretic results on spanning tree enumeration in symmetric graphs may be applied to calculate determinants of simple theta curves.
Rights
© The Author
Is Part Of
VCU University Archives
Is Part Of
VCU Theses and Dissertations
Date of Submission
7-19-2024