{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/28405"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/28405","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"The Quantum Automorphism Group and Undirected Trees","abstract":"A classification of all undirected trees with automorphism group isomorphic to $(Z_2)^l$ is given in terms of a vertex partition called a refined star partition. Recently the notion of a quantum automorphism group has been defined by T. Banica and J. Bichon. The quantum automorphism group is similar to the classical automorphism group, but has relaxed commutivity. The classification of all undirected trees with automorphism group isomorphic to $(Z_2)^l$ along with a similar classification of all undirected asymmetric trees is used to give some insight into the structure of the quantum automorphism group for such graphs.","abstract_html":"A classification of all undirected trees with automorphism group isomorphic to <span class=\"etd-inline-math\">(Z<sub>2</sub>)<sup>l</sup></span> is given in terms of a vertex partition called a refined star partition. Recently the notion of a quantum automorphism group has been defined by T. Banica and J. Bichon. The quantum automorphism group is similar to the classical automorphism group, but has relaxed commutivity. The classification of all undirected trees with automorphism group isomorphic to <span class=\"etd-inline-math\">(Z<sub>2</sub>)<sup>l</sup></span> along with a similar classification of all undirected asymmetric trees is used to give some insight into the structure of the quantum automorphism group for such graphs.","abstract_has_math":true,"creators":["Fulton, Melanie B."],"institution":"Virginia Tech","degree_name":"Ph. 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