Abstract
The fixing number of a graph Γ is the minimum number of labeled vertices that, when fixed, remove all nontrivial automorphisms from the automorphism group of Γ. The fixing set of a finite group G is the set of all fixing numbers of graphs whose automorphism groups are isomorphic to G. Previously, authors have studied the fixing sets of both abelian groups and symmetric groups. In this article, we determine the fixing set of the dihedral group.
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