Communications Project

Document Type:Master's Thesis
Name:Karen Sue Potanka
Title:Groups, Graphs, and Symmetry-Breaking
Degree:Master of Science
Committee Chair: Dr. Ezra Brown
Committee Members:Dr. Joseph Ball
Dr. Monte Boisen
Keywords:Petersen Graph, Symmetry-Breaking, Graph Theory
Date of defense:April 16, 1998
Availability:Release the entire work immediately worldwide.


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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