具有两个弧轨道有向图的点连通性

The Connectivity with two arc Orbits of Directed Graph

图D是带有两个弧轨道的强连通有向图,D1与D2是图D在自同构Aut(D)作用在边集E(D)上的两个弧轨道,有:D1=D[E1];D2=D[E2]为D的两个弧传递部分.我们证明,图D的弧连通度等于最小度,并且图D的点连通度,当加入围长条件,如果满足g(G)≥δ(D)-1/δ(Di)+1;则κ(D)=δ(D),这里我们只考虑δ(Di)≥0(i=1,2)的情况,并且δ(Di)是Di的最小度;κ(D)是有向图D的点连通度.

Let D be a strongly connected digraph with two arc orbits, D1 and D2 be its arc orbits under the action of Aut （D） on E（D）. Let D1 = D[ Eli and D2 = D[ E2] ,Which are called the arc transitive parts of D. It is proved that the arc connectivity was its minimum degree. And for the vertex connectivity of graph, when thecondition of the girth is added, it is inferred K（D） =δ（D） ifg（G） ≥δ（D）-1/δ（D1）＋1. Under only considering the case where δ（Di） 1〉 0 （i = 1,2） and 8（ Di ） is the minimum degree of Di;K （D） is the minimum degree of Di and K （D） is the vertex connectivity of D.