The 3-Extra Connectivity of the Data Center Network BCube. (5th October 2021) - Yi, Yi; Fan, Jianxi; Cheng, Baolei; Wang, Yan; Yu, Jia
Abstract: Connectivity is a significant metric to assess the fault tolerance of a network. For a faulty vertex set $H$, the $h$ -extra connectivity is defined under the assumption that every component of the network removing $H$ has at least $h+1$ fault-free vertices. Compared to the traditional connectivity, which is defined under the assumption that the network removing $H$ is disconnected or trivial, the $h$ -extra connectivity can better reflect the true fault tolerance of the network. The $BCube$ is an important server-centric data center network; it has good fault tolerance and scalability. In this paper, our research focuses on the logical structure of $BCube$, named $BC_{n, k}$, which is actually a specific type of generalized hypercubes. We prove that the 3-extra connectivity of $BC_{n, k}$ is $4(k+1)(n-1)-4n$ for $k≥ 4$ and $n≥ 4$ .