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Groups, Graphs, and Symmetry-Breaking

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dc.contributor.authorPotanka, Karen Sueen
dc.contributor.committeechairBrown, Ezra A.en
dc.contributor.committeememberBoisen, Monte B. Jr.en
dc.contributor.committeememberBall, Joseph A.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T20:51:19Zen
dc.date.adate1998-04-28en
dc.date.available2014-03-14T20:51:19Zen
dc.date.issued1998-04-16en
dc.date.rdate1998-04-28en
dc.date.sdate1998-04-16en
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(D<sub>n</sub>) is found where D<sub>n</sub> 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
dc.description.degreeMaster of Scienceen
dc.identifier.otheretd-32798-215247en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-32798-215247/en
dc.identifier.urihttp://hdl.handle.net/10919/36630en
dc.publisherVirginia Techen
dc.relation.haspartetd.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectPetersen Graphen
dc.subjectSymmetry-Breakingen
dc.subjectGraph Theoryen
dc.titleGroups, Graphs, and Symmetry-Breakingen
dc.typeThesisen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.levelmastersen
thesis.degree.nameMaster of Scienceen

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