Conditional (t,k) -Diagnosis in Regular and Irregular Graphs Under the Comparison Diagnosis Model - 2018


Assume that there are at most t faulty vertices. A system is conditionally (t, k)-diagnosable if a minimum of k faulty vertices (or all faulty vertices if fewer than k faulty vertices stay) can be identified in every iteration underneath the assumption that each vertex is adjacent to at least one fault-free vertex. Let ? c (G) be the conditional vertex connectivity of G, which measures the vertex connectivity of G according to the assumption that each vertex is adjacent to at least one fault-free vertex. Let ?(G) be the utmost degrees of the given graph G. When a graph G satisfies the condition that for any combine of vertices with distance two has a minimum of 2 common neighbors in G, we have a tendency to show the subsequent 2 results: one) An r-regular network G containing N vertices is conditionally (r+1/n+v (r+one)(r-1) / 4x(G)N) 2, k c (G)) diagnosable, where r = 3 and N = 4x(G)/(r+1)(25r-9). a pair of) An irregular network G containing N vertices is conditionally (?(G)+one/N-1, kc(G))-diagnosable. By applying the on top of results to multiprocessor systems, we have a tendency to can live conditional (t, k)-diagnosabilities for augmented cubes, folded hypercubes, balanced hypercubes, and exchanged hypercubes.

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