{1, 2, 3}-Restricted Connectivity of $(n, k)$-Enhanced Hypercubes. (13th November 2019) - Yu, Hui; Yang, Jiejie; Lin, Limei; Huang, Yanze; Li, Jine; Chen, Riqing
Abstract: The connectivity of a graph is a classic measure for fault tolerance of the network. Restricted connectivity measure is a crucial subject for a multiprocessor system's ability to tolerate fault processors, and improves the connectivity measurement accuracy. Furthermore, if a network possesses a restricted connectivity property, it is more reliable with a lower vertex failure rate compared with other networks. The $\left (n, k\right )$ -dimensional enhanced hypercube, denoted by $Q_{n, k}$, a variant of hypercube, which is a well-known interconnection network. In this paper, we analyze the fault tolerant properties for $\left (n, k\right )$ -enhanced hypercube, and establish the $1$ -restricted connectivity of $Q_{n, k} (n\ge k+1)$ and $\{2, 3\}$ -restricted connectivity of $(n, k)$ -enhanced hypercube $Q_{n, k} (n=k+1)$ . Furthermore, we propose the tight upper bound of $\{2, 3\}$ -restricted connectivity of $Q_{n, k} (n> k+1)$ . Moreover, we show many figures to better illustrate the process of the proofs.