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A Survey of Methods to Determine Quantum Symmetry of Graphs

Phillips, Samantha
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.
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2021-05-01
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Undergraduate Honors Theses
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Swartz, Eric
Clare, Pierre
Lewis, Robert Michael
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Mathematics
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https://scholarworks.wm.edu/handle/internal/11157
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