Super-connected and Hyper-connected Cubic Bi-Cayley Graphs

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 ff 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.