The diagnosability of a system is defined as the maximum number of faulty processors that the system can guarantee to identify, which plays an important role in measuring of the reliability of multiprocessor systems. In the work of Peng et al. in 2012, they proposed a new measure for fault diagnosis of systems, namely, $g$ -good-neighbor conditional diagnosability. It is defined as the diagnosability of a multiprocessor system under the assumption that every fault-free node contains at least $g$ fault-free neighbors, which can measure the reliability of interconnection networks in heterogeneous environments more accurately than traditional diagnosability. The $k$ -ary $n$ -cube is a family of popular networks. In this study, we first investigate and determine the $R_g$ -connectivity of $k$ -ary $n$ -cube for $0\le g\le n.$ Based on this, we determine the $g$ -good-neighbor conditional diagnosability of $k$ -ary $n$ -cube under the PMC model and MM* model for $k\ge 4, n\ge 3$ and $0\le g\le n.$ Our study shows the $g$ -good-neighbor conditional diagnosability of $k$ -ary $n$ -cube is several times larger than the classical diagnosability of $k$ -ary $n$ -cube.

/pdf/the-schmi-g-good-neighbor-conditional-diagnosability-of-15um3hpd5g.pdf

The ${\schmi g}$ -Good-Neighbor Conditional Diagnosability of ${\schmi k}$ -Ary ${\schmi n}$ -Cubes under the PMC Modeland MM* Model

Conditional connectivity of Cayley graphs generated by transposition trees

{2,3}-Extraconnectivities of hypercube-like 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 $1\le g\le 3$ . 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.

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

The 2-Extra Connectivity and 2-Extra Diagnosability of Bubble-Sort Star Graph Networks

A kind of conditional vertex connectivity of star graphs

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A kind of conditional vertex connectivity of star graphs