On the g-extra diagnosability of enhanced hypercubes

Abstract

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 Qn,k,n≥3,k∈[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−(g2)+1 in terms of the PMC diagnostic model for g∈[1,min⁡{(n−3)/2,k−3}],n≥2g+3, and k∈[max⁡{4,g+3},n−1]; as well as g∈[1,(n−5)/2], and n=k; and that in terms of MM* model, when g∈[2,min⁡{(n−3)/2,k−3}], n≥2g+3, and k∈[max⁡{4,g+3},n−1]; as well as g∈[2,(n−5)/2], and n=k.