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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.