Distinguishing geometric graphs

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Distinguishing geometric graphs
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 rdistinguishing 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 any distinguishing number between 1 and n inclusive. Finally we show that every K3,3 can be 2-distinguished. We also offer several open questions.
Michael O. Albertson, Debra L. Boutin
Added 13 Dec 2010
Updated 13 Dec 2010
Type Journal
Year 2006
Where JGT
Authors Michael O. Albertson, Debra L. Boutin
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