h-Restricted Connectivity of BCuben,k Data Center Networks

h-restricted connectivity of simple graph $G$ proposed by [1], denoted by k^h(G), is defined as the minimum number of elements in vertex set $F$ of $G$ such that $G$ - $F$ is disconnected, and the degree of each vertex in $G$ - $F$ is at least h. The n-dimensional BCube with k-port switches denoted as BCuben,k, is one of the most attractive data center networks to support the growing needs of cloud computing and big data. The $h$-restricted connectivity of a data center network is directly related to its reliability and fault tolerability of it, so it is an important indicator to evaluate the robustness of the network. In this paper, we focus ourselves on h-restricted connectivity of BCuben,k, and reveal that k^h(BCuben,k) = pk^r(k - 1)(n - r - 1) + k^r (k - p) for h = r(k - 1) + (p - 1), where p < k, k ≥ 2 and n ≥ r + 4, which improves the result in [2].