The Extra, Restricted Connectivity and Conditional Diagnosability of Split-Star Networks

Connectivity is a classic measure for fault tolerance of a network in the case of vertices failures. Extra connectivity and restricted connectivity are two important indicators of the robustness of a multi-processor system in presence of failing processors. An interconnection network's diagnosability is an important measure of its self-diagnostic capability. The conditional diagnosability is widely accepted as a new measure of diagnosability by assuming that any fault-set cannot contain all neighbors of any node in a multiprocessor system. In this paper, we analyze the combinatorial properties and fault tolerance ability for the Split-Star Network, denoted by S-n(2), a well-known interconnection network proposed for multiprocessor systems, establish the g-extra connectivity, where 1 <= g <= 3. We also determine the h-restricted connectivity (h = 1,2), and prove that the conditional diagnosability of S-n(2) (n >= 4) is 6n - 16 under the comparison model, which is about three times of the S-n(2)'s traditional diagnosability. As a product, the strong diagnosability of S-n(2) is also obtained.