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The distinguishing number, a measure of relative symmetry

Michael Albertson
Smith College

Thursday, May 10, 2007
007 Kemeny Hall, 4 pm
Tea 3:30 pm, 300 Kemeny Hall

Abstract: Suppose a group acts on a set X. A coloring of the elements of X using r colors is said to be r-distinguishing if the only group element that preserves the coloring is the identity. The smallest r for which there is an r-distinguishing coloring is called the distinguishing number of X. Distinguishing was introduced about ten years ago by Albertson and Collins in the case when the group is the automorphism group of a graph X. During the past three years there have been some extraordinary advances. This talk will introduce the subject, present some recent highlights, and present several provocative (I hope) open questions.

This talk will be accessible to graduate students.