Generalized measures of fault tolerance in exchanged hypercubes

The exchanged hypercube 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 Q(s+t+1). This paper considers a kind of generalized measures kappa((h)) and lambda((h)) of fault tolerance in EH(s,t) with 1 <= s <= t and determines kappa((h))(EH(s,t))=lambda((h)) (EH(s, t)) = 2(h)(s + 1 - h) for any h with 0 <= h <= s. The results show that at least 2(h) (s + 1 - h) vertices (resp. 2(h) (s + 1 - h) edges) of 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. (C) 2013 Elsevier B.V. All rights reserved.