Fault diagnosability of data center networks

Abstract

A kind of generalization of diagnosability for a network G is g-good-neighbor diagnosability which is denoted by tg(G). Let κg(G) be the Rg-connectivity. Lin et al. (2016) [17] and Xu et al. (2017) [29] gave the same problem independently that: the relationship between the Rg-connectivity κg(G) and tg(G) of a general graph G needs to be studied in the future. In this paper, this open problem is solved for general regular graphs. We firstly establish the relationship of κg(G) and tg(G), and obtain that tg(G)=κg(G)+g under some conditions. Secondly, we obtain the g-good-neighbor diagnosability of data center network Dk,n which are tg(Dk,n)=(g+1)(k−1)+n+g for 1≤g≤n−1 under the PMC model and the MM* model, respectively. Furthermore, we show that Dk,n is tightly super (n+k−1)-connected for n≥2 and k≥2 and we also prove that the largest connected component of the survival graph contains almost all of the remaining vertices in Dk,n when n+2k−2 vertices removed.