کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4650083 1342473 2009 6 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Distinguishing labeling of group actions
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
Distinguishing labeling of group actions
چکیده انگلیسی

Suppose ΓΓ is a group acting on a set XX. An rr-labeling f:X→{1,2,…,r}f:X→{1,2,…,r} of XX is distinguishing (with respect to ΓΓ) if the only label preserving permutation of XX in ΓΓ is the identity. The distinguishing number, DΓ(X)DΓ(X), of the action of ΓΓ on XX is the minimum rr for which there is an rr-labeling which is distinguishing. This paper investigates the relation between the cardinality of a set XX and the distinguishing numbers of group actions on XX. For a positive integer nn, let D(n)D(n) be the set of distinguishing numbers of transitive group actions on a set XX of cardinality nn, i.e., D(n)={DΓ(X):|X|=n and Γ acts transitively on X}D(n)={DΓ(X):|X|=n and Γ acts transitively on X}. We prove that |D(n)|=O(n). Then we consider the problem of an arbitrary fixed group ΓΓ acting on a large set. We prove that if for any action of ΓΓ on a set YY, for each proper normal subgroup HH of ΓΓ, DH(Y)≤2DH(Y)≤2, then there is an integer nn such that for any set XX with |X|≥n|X|≥n, for any action of ΓΓ on XX with no fixed points, DΓ(X)≤2DΓ(X)≤2.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Mathematics - Volume 309, Issue 6, 6 April 2009, Pages 1760–1765
نویسندگان
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