Year
2018
Season
Spring
Paper Type
Master's Thesis
College
College of Arts and Sciences
Degree Name
Master of Science in Mathematical Sciences (MS)
Department
Mathematics & Statistics
NACO controlled Corporate Body
University of North Florida. Department of Mathematics and Statistics
First Advisor
Dr. Daniela Genova
Second Advisor
Dr. Michelle DeDeo
Rights Statement
http://rightsstatements.org/vocab/InC/1.0/
Third Advisor
Dr. Sami Hamid
Department Chair
Dr. Richard Patterson
College Dean
Dr. George Rainbolt
Abstract
DNA graph structures can self-assemble from branched junction molecules to yield solutions to computational problems. Self-assembly of graphs have previously been shown to give polynomial time solutions to hard computational problems such as 3-SAT and k-colorability problems. Jonoska et al. have proposed studying self-assembly of graphs topologically, considering the boundary components of their thickened graphs, which allows for reading the solutions to computational problems through reporter strands. We discuss weighting algorithms and consider applications of self-assembly of graphs and the boundary components of their thickened graphs to problems involving minimal weight Eulerian walks such as the Chinese Postman Problem and the Windy Postman Problem.
Suggested Citation
Bakewell, Katie, "Self-Assembly of DNA Graphs and Postman Tours" (2018). UNF Graduate Theses and Dissertations. 857.
https://digitalcommons.unf.edu/etd/857
Included in
Discrete Mathematics and Combinatorics Commons, Geometry and Topology Commons, Other Mathematics Commons