caa a22 4500 445358645 CHVBK 20180317142908.0 cr unu---uuuuu 170323e20111101xx s 000 0 eng 10.1007/s00493-011-2221-7 doi (NATIONALLICENCE)springer-10.1007/s00493-011-2221-7 Distinguishing labeling of the actions of almost simple groups [Elektronische Daten] [Ákos Seress, Tsai-Lien Wong, Xuding Zhu] 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 x∈X 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. János Bolyai Mathematical Society and Springer Verlag, 2011 Seress Ákos Centre for the Mathematics of Symmetry and Computation, The University of Western Australia, 6009, Crawley, WA, Australia aut Wong Tsai-Lien Department of Applied Mathematics, National Sun Yat-sen University, 80424, Kaohsiung, Taiwan aut Zhu Xuding Department of Mathematics, Zhejiang Normal University, Jinhua, China aut Combinatorica Springer-Verlag 31/4(2011-11-01), 489-506 0209-9683 31:4<489 2011 31 493 https://doi.org/10.1007/s00493-011-2221-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00493-011-2221-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Seress Ákos Centre for the Mathematics of Symmetry and Computation, The University of Western Australia, 6009, Crawley, WA, Australia aut NATIONALLICENCE 700 1- Wong Tsai-Lien Department of Applied Mathematics, National Sun Yat-sen University, 80424, Kaohsiung, Taiwan aut NATIONALLICENCE 700 1- Zhu Xuding Department of Mathematics, Zhejiang Normal University, Jinhua, China aut NATIONALLICENCE 773 0- Combinatorica Springer-Verlag 31/4(2011-11-01), 489-506 0209-9683 31:4<489 2011 31 493 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer