On fixity of arc-transitive graphs

被引：0
作者：
Florian Lehner
Primož Potočnik
Pablo Spiga
机构：
[1] Graz University of Technology,Institute of Discrete Mathematics
[2] University of Ljubljana,Faculty of Mathematics and Physics
[3] University of Milano-Bicocca,Dipartimento di Matematica Pura e Applicata
来源：
Science China Mathematics | 2021年 / 64卷
关键词：
permutation group; fixity; minimal degree; graph; automorphism group; vertex-transitive; arc-transitive; fixed points; 20B25;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The relative fixity of a permutation group is the maximum proportion of the points fixed by a non-trivial element of the group, and the relative fixity of a graph is the relative fixity of its automorphism group, viewed as a permutation group on the vertex-set of the graph. We prove in this paper that the relative fixity of connected 2-arc-transitive graphs of a fixed valence tends to 0 as the number of vertices grows to infinity. We prove the same result for the class of arc-transitive graphs of a fixed prime valence, and more generally, for any class of arc-transitive locally-L graphs, where L is a fixed quasiprimitive graph-restrictive permutation group.
引用
收藏
页码：2603 / 2610
页数：7
相关论文
共 40 条
[1]  
Babai L(1981)On the order of uniprimitive permutation groups Ann of Math (2) 113 553-568
[2]  
Babai L(2015)On the automorphism groups of strongly regular graphs II J Algebra 421 560-578
[3]  
Burness T(2007)Fixed point ratios in actions of finite classical groups I J Algebra 309 69-79
[4]  
Conder M(2011)Motion and distinguishing number two Ars Math Contemp 4 63-72
[5]  
Tucker T(1973)Arc-transitivity in graphs Q J Math 24 399-407
[6]  
Gardiner A(2014)A class of semiprimitive groups that are graph-restrictive Bull Lond Math Soc 46 1226-1236
[7]  
Giudici M(2015)On locally semiprimitive graphs and a theorem of Weiss J Algebra 427 104-117
[8]  
Morgan L(1998)On the minimal degree of a primitive permutation group J Algebra 207 127-145
[9]  
Giudici M(1967)Intersection matrices for finite permutation groups J Algebra 6 22-42
[10]  
Morgan L(2019)Odd extensions of transitive groups via symmetric graphs—The cubic case J Combin Theory Ser B 136 170-192
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