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Summary: Distinguishing Geometric Graphs
August 31, 2004
Michael O. Albertson 1
Department of Mathematics
Smith College, Northampton MA 01063
albertson@smith.edu
Debra L. Boutin
Department of Mathematics
Hamilton College, Clinton, NY 13323
dboutin@hamilton.edu
Abstract
We begin the study of distinguishing geometric graphs. Let G
be a geometric graph. An automorphism of the underlying graph
that preserves both crossings and noncrossings is called a geometric
automorphism. A labelling, f : V (G) {1, 2, . . . , r}, is said to be r-
distinguishing if no nontrivial geometric automorphism preserves the
labels. The distinguishing number of G is the minimum r such that G
has an r-distinguishing labelling. We show that when Kn is not the
nonconvex K4, it can be 3-distinguished. Furthermore when n 6,
there is a Kn that can be 1-distinguished. For n 4, K2,n can realize
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