Super connectivity of balanced hypercubes

The reliability of an interconnection network is an important issue for multiprocessor systems. In this paper, we study a reliability measure, called super connectivity, in the balanced hypercube BHnBHn, which is a variant of the hypercube. We show that the super connectivity of BHnBHn is 4n-44n-4 and the super edge-connectivity of BHnBHn is 4n-24n-2 for n⩾2n⩾2. That is, to become a disconnected graph containing no isolated vertex, we need to remove at least 4n-44n-4 vertices (resp. 4n-24n-2 edges) from BHnBHn.