Abstract
The Rh-restricted connectivity κh is a significant measurement to estimate the reliability of large-scale processor system. The arrangement graph An,k is a generalization and also a competitive alternative of the star graph Sn. In this paper, for any non-negative integer h≤n−2, we determine that κh(An,2)=n(n−2)/2 provided h is odd with h=n−3, otherwise κh(An,2)=(h+2)(n−2)−⌊h2/2+h⌋. This result implies the upper bound of κh(An,k) given by Cheng et al. (J. Supercomput., 73(8)(2017) 3669–3682) is not optimal in a sense.
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