论文标题
关于电弧传输图的固定性
On fixity of arc-transitive graphs
论文作者
论文摘要
置换组的相对固定性是该组的非平凡元素固定的点的最大比例，图形的相对固定性是其自动形态组的相对固定性，被视为图形基因的置换组。我们在本文中证明，随着顶点的数量增长到无穷大，固定价的$ 2 $ -ARC传递图的相对固定性往往$ 0 $。我们证明了固定质量价的ARC传递图的结果相同，更普遍地，对于任何类别的ARC传输本地 - $ L $图形，其中$ l $是固定的准图形驱动式置换组。
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.
