A Pessimistic Fault Diagnosability of Large-Scale Connected Networks via Extra Connectivity

The t/kt/k-diagnosability and hh-extra connectivity are regarded as two important indicators to improve the network reliability. The t/kt/k-diagnosis strategy can significantly improve the self-diagnosing capability of a network at the expense of no more than kk fault-free nodes being mistakenly diagnosed as faulty. The hh-extra connectivity can tremendously improve the real fault tolerability of a network by insuring that each remaining component has no fewer than h+1h+1 nodes. However, there is few result on the inherent relationship between these two indicators. In this article, we investigate the reason that caused the serious flawed results in (Liu, 2020), and we propose a diagnosis algorithm to establish the t/kt/k-diagnosability for a large-scale connected network GG under the PMC model by considering its hh-extra connectivity. Let \kappa h(G)κh(G) be the hh-extra connectivity of GG. Then, we can deduce that GG is \kappa h(G)/hκh(G)/h-diagnosable under the PMC model with some basic conditions. All \kappa h(G)κh(G) faulty nodes can be correctly diagnosed in the large-scale connected network GG and at most hh fault-free nodes would be misdiagnosed as faulty. The complete fault tolerant method adopts combinatorial properties and linearly many fault analysis to conquer the core of our proofs. We will apply the newly found relationship to directly obtain the \kappa h(G)/hκh(G)/h-diagnosability of a series of well known networks, including hypercubes, folded hypercubes, balanced hypercubes, dual-cubes, BC graphs, star graphs, Cayley graphs generated by transposition trees, bubble-sort star graphs, alternating group graphs, split-star networks, kk-ary nn-cubes and (n,k)(n,k)-star graphs.