The g-good-neighbor diagnosability of (n,k)-star graphs

Fault diagnosability of data center networks

“…Xu et al [23] and Lin et al [34] 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.…”

A Complete Classification of Which (n, k)-Star Graphs are Cayley Graphs

“…There has been much research on the class of (n, k)-star graphs studying embeddings, broadcasting, Hamiltonicity and surface area as well as their applicability in theoretical computer science. Recent papers (within the past 3 years) include [4,5,7,8,10,13,17,20,23,28,29]. The first major result on Hamiltonicity was given in [17], which proves that (n, k)-star graphs are Hamiltonian; in fact, an (n, k)-star graph remains Hamiltonian if n − 3 vertices and/or edges are deleted.…”

On g-good-neighbor conditional diagnosability of (n,k)-star networks

“…In recent years, S n,k has received considerable attention [4, 7-9, 13, 16, 17, 25, 31]. In particular, Xu et al [25] derived the following result about the g-good-neighbor conditional diagnosability of S n,k under the PMC model and the MM * model. Theorem 1.1 (Xu et al [25]) The g-good-neighbor conditional diagnosabilities of the (n, k)star graph S n,k under the PMC model and the MM * model are…”

“…However, there are some unknown cases (see Table 1). [25] n (PMC) [25] n + k − 2 [25] 2n − 3 [14,25] ? (n = 3) ?…”

“…(n = 3) ? (n ≥ 3, MM * ) 2 ≤ g ≤ n 2 − 1 n 2 − 1 [25] n + g(k − 1) − 1 [25] n 2 ≤ g ≤ n − k ? (n − g)(g + 1)!…”