One of the important issues in evaluating an interconnection network is to study the Hamiltonian cycle embedding problems. For a positive integer k, a graph G is said to be spanning k-cyclable if for k prescribed vertices , there exist k disjoint cycles such that the union of spans G, and each contains exactly one vertex of . According to the definition, the problem of finding hamiltonian cycle focuses on k = 1. The notion of spanning cyclability can be applied to the problem of identifying faulty processors and other related issues in interconnection networks. The n-dimensional augmented cube is an important node-symmetric variant of the n-dimensional hypercube . In this paper, we prove that with is spanning k-cyclable for .

The pessimistic diagnosability of Split-Star Networks under the PMC model

Diagnosable evaluation of enhanced optical transpose interconnection system networks

The pessimistic diagnosability of alternating group graphs under the PMC model

Fault isolation and identification in general biswapped networks under the PMC diagnostic model

Fault diagnosability of arrangement graphs

The growing size of the multiprocessor system increases its vulnerability to component failures. It is crucial to locate and replace the faulty processors to maintain a system's high reliability. The fault diagnosis is the process of identifying faulty processors in a system through testing. This paper shows that the largest connected component of the survival graph contains almost all of the remaining vertices in the dual-cube DCnwhen the number of faulty vertices is up to twice or three times of the traditional connectivity. Based on this fault resiliency, this paper determines that the conditional diagnosability of DCn(n ≥ 3) under the comparison model is 3n − 2, which is about three times of the traditional diagnosability.

The design of large dependable multiprocessor systems requires quick and precise mechanisms for detecting the faulty nodes. The system-level fault diagnosis is the process of identifying faulty processors in a system through testing. This paper shows that the largest connected component of the survival graph contains almost all remaining vertices in the hierarchical hypercube HHC n when the number of faulty vertices is up to two or three times of the traditional connectivity. Based on this fault resiliency, we establish that the conditional diagnosability of HHC n (n=2 m +m, m≥2) under the comparison model is 3m−2, which is about three times of the traditional diagnosability.

The conditional fault diagnosability of (n, k)-star graphs

The growing size of the multiprocessor systems increases their vulnerability to component failures. It is crucial to locate and replace the faulty processors to maintain the system's high reliability. The fault diagnosis is the process of identifying faulty processors in a system through testing. The conditional diagnosis requires that for each processor v in a system, all the processors that are directly connected to v do not fail simultaneously. In this paper, we show that the conditional diagnosability of the crossed cubes CQ n under the comparison diagnosis model is 3n−5 when n≥7. Hence, the conditional diagnosability of CQ n is three times larger than its classical diagnosability.

Diagnosability of the Incomplete Star Graphs

In this article, we consider the problem of self-diagnosis of multiprocessor and multicomputer systems under the generalized comparison model. In this approach, a system consists of a collection n independent heterogeneous processors (or units) interconnected via point-to-point communication links, and it is assumed that at most t of these processors are permanently faulty. For the purpose of diagnosis, system tasks are assigned to pairs of processors and the results are compared. The agreements and disagreements among units are the basis for identifying faulty processors. Such a system is said to be t-diagnosable if, given any complete collection of comparison results, the set of faulty processors can be unambiguously identified. We present an efficient fault identification method based on genetic algorithms. Analysis and simulations are provided, first, to evaluate the genetic parameters of the diagnosis algorithm; second, to show the efficiency of the genetic approach. The new strategy is shown to correctly identify the set of faulty processors, making it an attractive and viable addition or alternative to present fault diagnosis techniques.

In this correspondence a system-level, comparison-based strategy for identifying faulty processors in a multiprocessor system is described. Unlike other strategies which have been proposed in the literature, the comparison approach is more efficient and relies on more realistic assumptions about the system under consideration. The new strategy is shown to correctly identify the set of faulty processors with a remarkably high probability, making it an attractive and viable addition or alternative to present fault diagnosis techniques.