The distinguishing number of the direct product and wreath product action

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The distinguishing number of the direct product and wreath product action

Let G be a group acting faithfully on a set X . The distinguishing number of the action of G on X , denoted DG(X ), is the smallest number of colors such that there exists a coloring of X where no nontrivial group element induces a colorpreserving permutation of X . In this paper, we consider the distinguishing number of two important product actions, the wreath product and the direct product. ...

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Definition 1.2 (Distinguishing number of a graph). Let Γ = (V,E) be a graph and let f : V → [r] be a coloring of the set of vertices by r colors. The map f need not be surjective, in fact when r > |V | it cannot be surjective. We say that f is r-distinguishing if the only automorphism of Γ that fixes the coloring f is the trivial automorphism. The distinguishing number of Γ is denoted by D(Γ) a...

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ژورنال

عنوان ژورنال: Journal of Algebraic Combinatorics

سال: 2006

ISSN: 0925-9899,1572-9192

DOI: 10.1007/s10801-006-0006-7