Abstract: 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. 

Key words: super-connected, hyper-connected, cubic, Bi-Cayley graphs