Date of Graduation
Summer 2017
Degree
Master of Science in Mathematics
Department
Mathematics
Committee Chair
Les Reid
Abstract
Cayley graphs are graphs associated to a group and a set of generators for that group (there is also an associated directed graph). The purpose of this study was to examine multiple examples of Cayley graphs through group theory, graph theory, and applications. We gave background material on groups and graphs and gave numerous examples of Cayley graphs and digraphs. This helped investigate the conjecture that the Cayley graph of any group (except Z_2) is hamiltonian. We found the conjecture to still be open. We found Cayley graphs and hamiltonian cycles could be applied to campanology (in particular, to the change ringing of bells).
Keywords
abstract algebra, group theory, Cayley's Theorem, Cayley graphs, campanology
Subject Categories
Algebra | Other Applied Mathematics | Other Mathematics
Copyright
© Anna Tripi
Recommended Citation
Tripi, Anna, "Cayley Graphs of Groups and Their Applications" (2017). MSU Graduate Theses/Dissertations. 3133.
https://bearworks.missouristate.edu/theses/3133
Open Access
