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dc.contributor.authorPotanka, Karen Sueen_US
dc.date.accessioned2014-03-14T20:51:19Z
dc.date.available2014-03-14T20:51:19Z
dc.date.issued1998-04-16en_US
dc.identifier.otheretd-32798-215247en_US
dc.identifier.urihttp://hdl.handle.net/10919/36630
dc.description.abstractA labeling of a graph G is said to be r-distinguishing if no automorphism of G preserves all of the vertex labels. The smallest such number r for which there is an r-distinguishing labeling on G is called the distinguishing number of G. The distinguishing set of a group Gamma, D(Gamma), is the set of distinguishing numbers of graphs G in which Aut(G) = Gamma. It is shown that D(Gamma) is non-empty for any finite group Gamma. In particular, D(Dn) is found where Dn is the dihedral group with 2n elements. From there, the generalized Petersen graphs, GP(n,k), are defined and the automorphism groups and distinguishing numbers of such graphs are given.en_US
dc.publisherVirginia Techen_US
dc.relation.haspartetd.pdfen_US
dc.rightsI hereby grant to Virginia Tech or its agents the right to archive and to make available my thesis or dissertation in whole or in part in the University Libraries in all forms of media, now or hereafter known. I retain all proprietary rights, such as patent rights. I also retain the right to use in future works (such as articles or books) all or part of this thesis or dissertation.en_US
dc.subjectPetersen Graphen_US
dc.subjectSymmetry-Breakingen_US
dc.subjectGraph Theoryen_US
dc.titleGroups, Graphs, and Symmetry-Breakingen_US
dc.typeThesisen_US
dc.contributor.departmentMathematicsen_US
thesis.degree.nameMaster of Scienceen_US
thesis.degree.levelmastersen_US
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen_US
dc.contributor.committeechairBrown, Ezra A.en_US
dc.contributor.committeememberBoisen, Monte B. Jr.en_US
dc.contributor.committeememberBall, Joseph A.en_US
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-32798-215247/en_US
dc.date.sdate1998-04-16en_US
dc.date.rdate1998-04-28
dc.date.adate1998-04-28en_US


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