The super connectivity of exchanged hypercubes

The exchanged hypercube EH(s,t)EH(s,t) where s⩾1s⩾1 and t⩾1t⩾1 are two positive integers, proposed by Loh et al. [The exchanged hypercube, IEEE Transactions on Parallel and Distributed Systems 16 (9) (2005) 866–874], is obtained by systematically removing links from a binary hypercube QnQn. This paper determines that the super connectivity and the super edge-connectivity of EH(s,t)EH(s,t) are 2s   where s⩽ts⩽t. That is, for s⩽ts⩽t, at least 2s vertices (resp. 2s   edges) of EH(s,t)EH(s,t) are removed to get a disconnected graph that contains no isolated vertex.

Research highlights
► The super connectivity of the exchanged hypercube EH(s,t)EH(s,t) is determined.
► The super edge connectivity of the exchanged hypercube EH(s,t)EH(s,t) is determined.