The Reliability of k-Ary n-Cube Based on Component Connectivity

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Article numberbxab054
Journal / PublicationComputer Journal
Online published20 May 2021
Publication statusOnline published - 20 May 2021

Abstract

Connectivity and diagnosability are two crucial subjects for a network's ability to tolerate and diagnose faulty processors. The r-component connectivity r(G) of a network G is the minimum number of vertices whose deletion results in a graph with at least r components. The r-component diagnosability ctr(G) of a network G is the maximum number of faulty vertices that the system can guarantee to identify under the condition that there exist at least r fault-free components. This paper first establishes that the (r + 1)-component connectivity of k-ary n-cube Qkn is r+1(Qkn) = −1/2r2 + (2n − 1/2)r + 1 for n ≥ 2, k ≥ 4 and 1 ≤ r n. In view of r+1(Qkn), we prove that the (r + 1)-component diagnosabilities of k-ary n-cube Qkn under the PMC model and MM* model are ctr+1(Qkn) = −1/2r2 + (2n − 3/2)r + 2n for n ≥ 4, k ≥ 4 and 1 ≤ r n − 1.

Research Area(s)

  • k-ary n-cube, reliability, component connectivity, component diagnosability, PMC model, MM* model, CONDITIONAL DIAGNOSABILITY, 2-EXTRA DIAGNOSABILITY, EXTRA CONNECTIVITY, NETWORKS

Citation Format(s)

The Reliability of k-Ary n-Cube Based on Component Connectivity. / LV, Mengjie; FAN, Jianxi; ZHOU, Jingya; YU, Jia; JIA, Xiaohua.

In: Computer Journal, 20.05.2021.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review