Date of Graduation

Summer 2017

Degree

Master of Science in Mathematics

Department

Mathematics

Committee Chair

Les Reid

Keywords

abstract algebra, group theory, Cayley's Theorem, Cayley graphs, campanology

Subject Categories

Algebra | Other Applied Mathematics | Other Mathematics

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).

Copyright

© Anna Tripi

Open Access

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