Type of Document	Master's Thesis
Author	Potanka, Karen Sue
Author's Email Address	kpotanka@vt.edu
URN	etd-32798-215247
Title	Groups, Graphs, and Symmetry-Breaking
Degree	Master of Science
Department	Mathematics
Advisory Committee	Advisor Name Title Brown, Ezra A. Committee Chair Ball, Joseph A. Committee Member Boisen, Monte B. Jr. Committee Member
Keywords	Petersen Graph Symmetry-Breaking Graph Theory
Date of Defense	1998-04-16
Availability	unrestricted
Abstract A 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.
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