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 pe...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.展开更多
基金supported by the Austrian Science Fund(FWF)Project W1230-N13.The second author was supported by the Research Programme P1-0294the Research Project J1-1691,both funded by the Slovenian Research Agency(ARRS).
文摘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.
