Abstract
The connectivity and diagnosability of a system or a network are two important measures. In 1996, Fabrega and Fiol proposed the h-extra connectivity of the network G = (V, E), which is necessary for (h, m)-diagnosability of networks. In 2016, Zhang et al. proposed the (h, m)-diagnosability of G that requires every component of G - S has at least (h + 1) nodes for S ⊆ 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 - 1/2h(h - 2n + 3) for n ≥ 5 and 0 ≤ h ≤ n -3, and m of the (h,m)-diagnosability of LTQ n is n - 1/2h(h - 2n + 1) for n ≥ 5, 0 ≤ h ≤ n - 3 in the PMC model and n ≥ 7, 0 ≤ h ≤ n - 3 in the MM* model, respectively.
Highlights
Many systems have networks as underlying topologies and a network is usually denoted by a graph where vertices denote processors and edges denote communication links between processors
The Preparata, Metze, and Chien’s (PMC) Model proposed by Preparata et al [20] and the Maeng and Malek’s (MM) model proposed by Maeng and Malek [18]
The special case, called the MM∗ model, of the MM model proposed by Sengupta and Dahbura [24]
Summary
Many systems have networks as underlying topologies and a network is usually denoted by a graph where vertices (nodes) denote processors and edges (links) denote communication links between processors. In 2005, Lai et al [13] introduced conditional diagnosability of the system They considered the situation that no faulty set can contain all the neighbors of any node in the system. Ren: h-Extra Connectivity and Diagnosability of Locally Twisted Cubes. Definition 5 [37]: For n ≥ 2, a locally twisted cube LTQn is defined recursively as follows: 1) LTQ2 is a graph consisting of four nodes labeled with 00, 01, 10 and 11, and four edges {00, 01}, {01, 11}, {11, 10} and {10, 00}. LTQn is an n-regular graph of 2n nodes and n2n−1 edges. THE EXTRA CONNECTIVITY OF THE LOCALLY TWISTED CUBE Firstly, we give some existing results.
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