34 research outputs found
Fault diagnosability of regular graphs
An interconnection network\u27s diagnosability is an important measure of its self-diagnostic capability. In 2012, Peng et al. proposed a measure for fault diagnosis of the network, namely, the -good-neighbor conditional diagnosability, which requires that every fault-free node has at least fault-free neighbors. There are two well-known diagnostic models, PMC model and MM* model. The {\it -good-neighbor diagnosability} under the PMC (resp. MM*) model of a graph , denoted by (resp. ), is the maximum value of such that is -good-neighbor -diagnosable under the PMC (resp. MM*) model. In this paper, we study the -good-neighbor diagnosability of some general -regular -connected graphs under the PMC model and the MM* model. The main result with some acceptable conditions is obtained, where is the girth of . Furthermore, the following new results under the two models are obtained: for the hierarchical star network , for the split-star networks and for the Cayley graph generated by the -tree
The Nature Diagnosability of Bubble-sort Star Graphs under the PMC Model and MM Model
Many multiprocessor systems have interconnection networks as underlying topologies and an interconnection network is usually represented by a graph where nodes represent processors and links represent communication links between processors. No fault set can contain all the neighbors of any fault-free vertex in the system, which is called the nature diagnosability of the system. Diagnosability of a multiprocessor system is one important study topic. As a famous topology structure of interconnection networks, the -dimensionalnbsp bubble-sort star graph nbsphas many good properties. In this paper, we prove that the nature diagnosability of nbspis nbspunder the PMC model for , the nature diagnosability of nbspis nbspunder the MM model for
Super edge-connectivity and matching preclusion of data center networks
Edge-connectivity is a classic measure for reliability of a network in the
presence of edge failures. -restricted edge-connectivity is one of the
refined indicators for fault tolerance of large networks. Matching preclusion
and conditional matching preclusion are two important measures for the
robustness of networks in edge fault scenario. In this paper, we show that the
DCell network is super- for and ,
super- for and , or and , and
super- for and . Moreover, as an application of
-restricted edge-connectivity, we study the matching preclusion number and
conditional matching preclusion number, and characterize the corresponding
optimal solutions of . In particular, we have shown that is
isomorphic to the -star graph for .Comment: 20 pages, 1 figur