http://staff.ustc.edu.cn/~xujm/200703.pdf

On reliability of the folded hypercubes

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

Maximally edge-connected and vertex-connected graphs and digraphs: A survey

Given a graph ${\mbi{G}}$ and a non-negative integer ${{g}}$ , the ${{g}}$ -extra connectivity (resp. ${{g}}$ -extra edge connectivity) of ${\mbi{G}}$ is the minimum cardinality of a set of vertices (resp. edges) in ${\mbi{G}}$ , if it exists, whose deletion disconnects ${\mbi{G}}$ and leaves each remaining component with more than ${{g}}$ vertices. This study shows that the 3-extra connectivity (resp. 3-extra edge connectivity) of an ${\mbi{n}}$ -dimensional folded hypercube is ${4}{{n}} - {5}$ for ${{n}} \geq {6}$ (resp. ${4}{{n}} - {4}$ for ${{n}} \geq {5}$ ). This study also provides an upper bound for the ${{g}}$ -extra connectivity on folded hypercubes for ${{g}} \geq {6}$ .

On 3-Extra Connectivity and 3-Extra Edge Connectivity of Folded Hypercubes

The conditional diagnosis is a very important measure of the reliability and the fault-tolerance of networks. The ‘condition’ means that no faulty set contains all neighbours of any node. Under this assumption, for any system G, every component of has more than 1 node, where F is the faulty set of G. The g-extra conditional diagnosability is defined under the assumption that every component of has more than nodes. ‘A system with at most t faulty nodes is defined as sequentially t-diagnosable if at least one faulty node can be repaired, so that the testing can be continued using the repaired node to eventually diagnose all faulty nodes’ [E.P. Duarte Jr., R.P. Ziwich, and L.C.P. Albini, A survey of comparison-based system-level diagnosis, ACM Comput. Surv. 433 2011, article 22]. To increase the degree of the sequential t-diagnosability of a system, sequential -diagnosis strategy is proposed in this paper. It is allowed that there are at most k misdiagnosed nodes. In this paper, we determine the g-extra conditional diagnosability of hypercubes and propose sequential -diagnosis algorithms for hypercubes with low time complexities under the Preparata, Metze, and Chien PMC model and the MM* model which is a special case of the Maeng and Malek MM model.

Jixiang Meng

Papers

Extraconnectivity of hypercubes

On a kind of restricted edge connectivity of graphs

Conditional connectivity of Cayley graphs generated by transposition trees

Structure fault tolerance of hypercubes and folded hypercubes

Connectivity of vertex and edge transitive graphs