1 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