The $h$ -Extra Connectivity and Diagnosability of Locally Twisted Cubes
Shiying Wang, Yunxia Ren · IEEE Access · 2019
The connectivity and diagnosability of a system or a network are two important measures. In 1996, Fàbrega and Fiol proposed the$h$-extra connectivity of the network$G=(V,E)$, which is necessary for$(h,m)$-diagnosability of networks. In 2016, Zhanget al.proposed the$(h,m)$-diagnosability of$G$that requires every component of$G-S$has at least$(h+1)$nodes for$S\subseteq V$. The locally twisted cube$LTQ_{n}$is applied widely. There are many studies on$LTQ_{n}$. In this paper, we show that the$h$-extra connectivity of$LTQ_{n}$is$n-\frac {1}{2}h(h-2n+3)$for$n\geq 5$and$0\leq h\leq n-3$, and$m$of the$(h,m)$-diagnosability of$LTQ_{n}$is$n-\frac {1}{2}h(h-2n+1)$for$n\geq 5$,$0\leq h\leq n-3$in the PMC model and$n\geq 7$,$0\leq h\leq n-3$in the MM$^{*}$model, respectively.