Generalized measures of fault tolerance in exchanged hypercubes

•We study generalized measures of fault tolerance of a network.•We consider the exchanged hypercube EH(s,t)EH(s,t).•We determine both h-connectivity and h  -edge-connectivity of H(s,t)H(s,t) are 2h(s+1−h)2h(s+1−h).•This result contains some known results and enhances EH(s,t)EH(s,t) as a network.

The exchanged hypercube EH(s,t)EH(s,t), proposed by Loh et al. [P.K.K. Loh, W.J. Hsu, Y. Pan, The exchanged hypercube, IEEE Transactions on Parallel and Distributed Systems 16 (9) (2005) 866–874], is obtained by removing edges from a hypercube Qs+t+1Qs+t+1. This paper considers a kind of generalized measures κ(h)κ(h) and λ(h)λ(h) of fault tolerance in EH(s,t)EH(s,t) with 1≤s≤t1≤s≤t and determines κ(h)(EH(s,t))=λ(h)(EH(s,t))=2h(s+1−h)κ(h)(EH(s,t))=λ(h)(EH(s,t))=2h(s+1−h) for any h   with 0≤h≤s0≤h≤s. The results show that at least 2h(s+1−h)2h(s+1−h) vertices (resp. 2h(s+1−h)2h(s+1−h) edges) of EH(s,t)EH(s,t) have to be removed to get a disconnected graph that contains no vertices of degree less than h, and generalizes some known results.