Abstract Diagnosability is an important metric to fault tolerance and reliability for multiprocessor systems. However, plenty of research on fault diagnosability focuses on node failure. In practical scenario, not only node failures take place but also link malfunctions may arise. In this work, we investigate the diagnosability of general regular networks with failing nodes as well as missing malfunctional links. Let $S$ be a set of the missing links and broken-down nodes. We first prove that the diagnosability of the survival graph $G\setminus S$ persists $\delta (G\setminus S)$ under the PMC model (Preparata, F.P., Metze, G. and Chien, R.T. (1967) On the connection assignment problem of diagnosable systems. IEEE Trans. Electron. Comput., EC-16, 848–854) for a $t$-regular and $t$-connected triangle-free network $G$ subject to $|S|\leq t-1$ and $|V(G)|\geq 3t-2$ ($t\geq 3$). Furthermore, we determine the diagnosability of $G\setminus S$ for some kinds of extensively explored $t$-regular networks with triangles subject to $|S|\leq t-1$ ($t\geq 3$).

Abstract In this paper, we propose a new digragh model for system level fault diagnosis, which is called the $(f_1,f_{2})$-bounded Preparata–Metze–Chien (PMC) model (shortly, $(f_1,f_{2})$-BPMC). The $(f_1,f_{2})$-BPMC model projects a system such that the number of faulty processors that test faulty processors with the test results $0$ does not exceed $f_{2}$$(f_2\leq f_{1})$ provided that the upper bound on the number of faulty processors is $f_{1}$. This novel testing model compromisingly generalizes PMC model (Preparata, F.P., Metze, G. and Chien R.T. (1967) On the connection assignment problem of diagnosable systems. IEEE Tran. Electron. Comput.,EC-16, 848–854) and Barsi–Grandoni–Maestrini model (Barsi, F., Grandoni, F. and Maestrini, P. (1976) A theory of diagnosability of digital systems. IEEE Trans. Comput.C-25, 585–593). Then we present some characterizations for one-step diagnosibility under the $(f_1,f_{2})$-bounded PMC model, and determine the diagnosabilities of some special regular networks. Meanwhile, we establish the characterizations of $f_1/(n-1)$-diagnosability and three configurations of $f_1/(n-1)$-diagnosable system under the $(f_1,f_{2})$-BPMC model.

Fault tolerance plays an important role in the interconnection networks, where permanent and intermittent faults are two kinds of fault situations. Permanent fault diagnosabilities of regular networks have been proposed widely while the intermittent fault diagnosabilities are also noteworthy. In this paper, we give a sufficient and necessary condition for k-regular k-connected graph Gn to be ti-diagnosable without repair in intermittent fault pattern. Detailly, we show that the intermittent fault diagnosability of Gn under the PMC model is k−⌈g−12⌉−2⁠, where g is the maximum number of common neighbors for any two distinct vertices. As applications, intermittent fault diagnosabilities of many famous networks are explored.

For a connected graph G=(V(G),E(G))⁠, a subset F⊂V(G) is called an Rk-vertex-cut if G−F is disconnected and each vertex u∈V(G)−F has at least k neighbors in G−F⁠. The cardinality of a minimum Rk-vertex-cut of G is the Rk-vertex-connectivity and is denoted by κk(G)⁠. The conditional connectivity is a new measure to study the fault tolerance of network structures beyond connectivity. In this paper, we study R1-vertex-connectivity and R2-vertex-connectivity of Cayley graphs generated by 2-trees T2,n⁠, which are denoted by KTn⁠, and show that κ1(KTn)=4n−8 for n≥4⁠; κ2(KTn)=8n−22 for n≥6⁠.