Fault diagnosability of data center networks

Abstract

The data center networks D n,k , proposed in 2008, has many desirable features such as high network capacity. A kind of generalization of diagnosability for network G is g-goodneighbor diagnosability which is denoted by t g (G). Let κ g (G) be the R g -connectivity. Lin et. al. in [IEEE Trans. on Reliability, 65 (3) (2016) 1248-1262] and Xu et. al in [Theor. Comput. Sci. 659 (2017) 53-63] gave the same problem independently that: the relationship between the R g -connectivity κ g (G) and t g (G) of a general graph G need to be studied in the future. In this paper, this open problem is solved for general regular graphs. We firstly establish the relationship of κ g (G) and t g (G), and obtain that t g (G) = κ g (G) + g under some conditions. Secondly, we obtain the g-good-neighbor diagnosability of D k,n which are t g (D k,n ) = (g + 1)(k − 1) + n + g for 1 ≤ g ≤ n − 1 under the PMC model and the MM model, respectively. Further more, we show that D k,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 D k,n when 2k +n−2 vertices removed.