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Combinatorica

, Volume 31, Issue 4, pp 489–506 | Cite as

Distinguishing labeling of the actions of almost simple groups

  • Ákos Seress
  • Tsai-Lien Wong
  • Xuding Zhu
Article
  • 83 Downloads

Abstract

Suppose Γ is a group acting on a set X, written as (Γ,X). An r-labeling f: X→{1,2, ..., r} of X is called distinguishing for (Γ,X) if for all σ∈Γ,σ≠1, there exists an element xX such that f(x)≠f(x σ ). The distinguishing number d(Γ,X) of (Γ,X) is the minimum r for which there is a distinguishing r-labeling for (Γ,X). If Γ is the automorphism group of a graph G, then d(Γ,V (G)) is denoted by d(G), and is called the distinguishing number of the graph G. The distinguishing set of Γ-actions is defined to be D*(Γ)={d(Γ,X): Γ acts on X}, and the distinguishing set of Γ-graphs is defined to be D(Γ)={d(G): Aut(G)≅Γ}. This paper determines the distinguishing set of Γ-actions and the distinguishing set of Γ-graphs for almost simple groups Γ.

Mathematics Subject Classification (2000)

20G15 05C25 20B25 

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Copyright information

© János Bolyai Mathematical Society and Springer Verlag 2011

Authors and Affiliations

  • Ákos Seress
    • 1
    • 4
  • Tsai-Lien Wong
    • 2
    • 5
  • Xuding Zhu
    • 3
  1. 1.Centre for the Mathematics of Symmetry and ComputationThe University of Western AustraliaCrawleyAustralia
  2. 2.Department of Applied MathematicsNational Sun Yat-sen UniversityKaohsiungTaiwan
  3. 3.Department of MathematicsZhejiang Normal UniversityJinhuaChina
  4. 4.Department of MathematicsThe Ohio State UniversityColumbusUSA
  5. 5.National Center for Theoretical SciencesTainanTaiwan

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