一些条件连通图的关系

在这篇文章中，我们主要研究一些条件连通图之间的关系，如上连通，上边连通，超连通和上混合连通．     

n重线有向图的超连通性

本文证明了，在最小度至少为3的前提下超弧连通有向图的迭代线图是超点连通的．作为推论，我们得到了Kautz网络和de Bruijn网络的超点连通性和超弧连通性．     

上连通和超连通的三次Bi-Cayley图

Let G be a finite group and let S(possibly, contains the identity element) be a subset of G. The Bi-Cayley graph BC(G, S) is a bipartite graph with vertex set G×{0, 1} and edge set {(g, 0) (sg, 1) : g∈G, s ∈ S}. A graph is said to be super-connected if every minimum vertex cut isolates a vertex. A graph is said to be hyper-connected if every minimum vertex cut creates two components, one of which is an isolated vertex. In this paper, super-connected and/or hyper-connected cubic Bi-Cayley graphs are characterized.