On the g-extra diagnosability of enhanced hypercubes

Several fault tolerant models have been investigated in order to study the fault-tolerance properties of self-diagnosable interconnection networks, which are often represented with a connected graph G. In particular, a g-extra cut of a non-complete graph G, g >= 0, is a set of vertices in G whose removal disconnects the graph, but every component in the survival graph contains at least g + 1 vertices. The g-extra diagnosability of G then refers to the maximum number of faulty vertices in G that can be identified when considering these g-extra faulty sets only. Enhanced hypercubes, denoted by Q(n,k), n >= 3, k is an element of[1, n], is another variant of the hypercube structure. In this paper, we make use of its super connectivity property to derive its g-extra diagnosability of (g + 1)n - ((g)(2)) + 1 in terms of the PMC diagnostic model for g is an element of [1, min{(n - 3)/2, k - 3}], n >= 2g + 3, and k is an element of [max{4, g + 3}, n - 1]; as well as g is an element of [1, (n - 5)/2], and n = k; and that in terms of MM* model, when g is an element of[2, min{(n - 3)/2, k - 3}], n >= 2g + 3, and k is an element of [max{4, g + 3}, n - 1]; as well as g is an element of[2, (n - 5)/2], and n = k. (c) 2022 Elsevier B.V. All rights reserved.