On fixity of arc-transitive graphs  

作　　者：Florian Lehner Primoz Potocnik Pablo Spiga 

机构地区：[1]Institute of Discrete Mathematics,Graz University of Technology,Graz 8010,Austria [2]Faculty of Mathematics and Physics,University of Ljubljana,Ljubljana 1000,Slovenia [3]Dipartimento di Matematica Pura e Applicata,University of Milano-Bicocca,Milano 20126,Italy

出　　处：《Science China Mathematics》2021年第12期2603-2610,共8页中国科学：数学（英文版）

基　　金：supported by the Austrian Science Fund(FWF)Project W1230-N13.The second author was supported by the Research Programme P1-0294;the Research Project J1-1691,both funded by the Slovenian Research Agency(ARRS).

摘　　要：The relative xity of a permutation group is the maximum proportion of the points xed by a non-trivial element of the group,and the relative xity of a graph is the relative xity of its automorphism group,viewed as a permutation group on the vertex-set of the graph.We prove in this paper that the relative xity of connected 2-arc-transitive graphs of a xed valence tends to 0 as the number of vertices grows to in nity.We prove the same result for the class of arc-transitive graphs of a xed prime valence,and more generally,for any class of arc-transitive locally-L graphs,where L is a xed quasiprimitive graph-restrictive permutation group.

关 键 词：permutation group xity minimal degree GRAPH automorphism group VERTEX-TRANSITIVE arc-transitive xed points 

分 类 号：O152.1[理学—数学] O157.5[理学—基础数学]