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

Abstract

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 $1\le g\le 3$ . We also determine the $h$ -restricted connectivity ( $h=1,2$ ), and prove that the conditional diagnosability of $S_n^2$ $(n\ge 4)$ 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.