Date Thesis Awarded
5-2021
Access Type
Honors Thesis -- Open Access
Degree Name
Bachelors of Science (BS)
Department
Mathematics
Advisor
Eric Swartz
Committee Members
Pierre Clare
Robert Michael Lewis
Abstract
We introduce the theory of quantum symmetry of a graph by starting with quantum permutation groups and classical automorphism groups. We study graphs with and without quantum symmetry to provide a comprehensive view of current techniques used to determine whether a graph has quantum symmetry. Methods provided include specific tools to show commutativity of generators of algebras of quantum automorphism groups of distance-transitive graphs; a theorem that describes why nontrivial, disjoint automorphisms in the automorphism group implies quantum symmetry; and a planar algebra approach to studying symmetry.
Recommended Citation
Phillips, Samantha, "A Survey of Methods to Determine Quantum Symmetry of Graphs" (2021). Undergraduate Honors Theses. William & Mary. Paper 1721.
https://scholarworks.wm.edu/honorstheses/1721
