Graph Distinguishability and the Generation of Non-Isomorphic Labellings

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dc.contributor.authorBird, William Herbert
dc.contributor.supervisorMyrvold, W. J.
dc.date.accessioned2013-08-26T22:26:49Z
dc.date.available2013-08-26T22:26:49Z
dc.date.copyright2013en_US
dc.date.issued2013-08-26
dc.degree.departmentDept. of Computer Scienceen_US
dc.degree.levelMaster of Science M.Sc.en_US
dc.description.abstractA distinguishing colouring of a graph G is a labelling of the vertices of G with colours such that no non-trivial automorphism of G preserves all colours. The distinguishing number of G is the minimum number of colours in a distinguishing colouring. This thesis presents a survey of the history of distinguishing colouring problems and proves new bounds and computational results about distinguishability. An algorithm to generate all labellings of a graph up to isomorphism is presented and compared to a previously published algorithm. The new algorithm is shown to have performance competitive with the existing algorithm, as well as being able to process automorphism groups far larger than the previous limit. A specialization of the algorithm is used to generate all minimal distinguishing colourings of a set of graphs with large automorphism groups and compute their distinguishing numbers.en_US
dc.description.proquestcode0984en_US
dc.description.proquestcode0405en_US
dc.description.proquestemailbbird@uvic.caen_US
dc.description.scholarlevelGraduateen_US
dc.identifier.urihttp://hdl.handle.net/1828/4839
dc.languageEnglisheng
dc.language.isoenen_US
dc.rights.tempAvailable to the World Wide Weben_US
dc.subjectDistinguishing Numberen_US
dc.subjectSims Tableen_US
dc.subjectSchreier-Sims Algorithmen_US
dc.subjectComputational Group Theoryen_US
dc.subjectGraph Algorithmsen_US
dc.subjectList-Distinguishing Colouringen_US
dc.subjectDistinguishing Colouringen_US
dc.subjectList-Distinguishing Numberen_US
dc.subjectCombinatorial Generationen_US
dc.subjectPermutation Groupsen_US
dc.titleGraph Distinguishability and the Generation of Non-Isomorphic Labellingsen_US
dc.typeThesisen_US

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