树在其自同构群下的点轨道集的特征

Features of vertices orbit of tree under its automorphism group

给定一棵有有限个顶点的无向、简单树,记作τ。把τ的自同构群,记作Autτ。a∈Vτ,定义A a={a i∈Vτ■α∈Autτ,使α(a i)=a},通过A a构造了树τ的子图τa=∪a,b∈Aa a≠bΓa,b,定义所有顶点之间的最大距离称为树τ的直径,记作diam(τ)。设diam(τa)=k≥0,k∈Z+,则■a,b∈A a,∈d(a,b)=k。并且c∈A a,有d(a,c)=k或者d(c,b)=k。

Given a simple undirected tree which has finite vertices, denoted τ as τ. We Denote auto-morphism group of τ as Autτ,for any a belongs to Vτ ,definite Aa = {ai∈Vτ｜ α∈Autτ,∈α（ai）=a}, we construct subgraph of τ with Aa , denoted τa =∪∨a,b∈Aa a≠b Гa,b,define diam （τ） as the maximum distance between all vertices called tree diameter. Assumed diam （τa）=k≥0,k∈Z^＋ , then there exist vertices a , b belonging toAa , such that d（a,b） = k. And for any vertice c that belongs to Ao ,wehaved（a,c） = kord（c,b） = k.