摘要 : The hierarchical star networks HS_n, proposed by Shi and Srimani, is a new level network topology and uses the star graphs as building blocks. Given a graph 6, the h-extra connectivity of 6 is the minimum cardinality of a set of v... 展开 The hierarchical star networks HS_n, proposed by Shi and Srimani, is a new level network topology and uses the star graphs as building blocks. Given a graph 6, the h-extra connectivity of 6 is the minimum cardinality of a set of vertices in G, if exists, whose deletion disconnects G and leaves every remaining component with more than h vertices. There is no known polynomial-time algorithm for finding κ_h,(G) for a given graph G. In this paper, by exploring the combinatorial properties and fault-tolerance of HS_n, we show that the largest component of a survival graph contains almost all of the remaining vertices after removing at most 4n-8 vertices and obtain the h-extra connectivity for 1 ≤ h ≤ 3 of HS_n, where n ≥ 5. As applications, the conditional diagnosability and the h-extra conditional diagnosability for 1 ≤ h ≤ 3 of HS_n under the PMC model and the MM* model, respectively, are obtained. 收起