Title page for ETD etd-32798-215247


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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