Structure fault-tolerance of divide-and-swap k-ary n-cube

As generalizations of classic connectivity, F-structure connectivity kappa (G; F) and F -substructure connectivity kappa(s)(G; F) are proposed to evaluate the reliability of networks. Let G be a graph, F be a connected subgraph of G and F = {F-1,F-2, ..., F-m} be a set of connected subgraphs of G. The F-structure connectivity (resp., F-substructure connectivity) of G, denoted by kappa (G; F) (resp., kappa(s)(G; F)), is the cardinality of a minimum F and F(i )is isomorphic to F (resp., a connected subgraph of F) for every 1 <= i <= m, and G - F is disconnected. The divide-and-swap cube DSC(n )is one of the most popular interconnection networks. In this paper, we generalize this network to divide-and-swap k-ary n-cube DSCnk, and study its topological structure and properties. Furthermore, we show that kappa (DSCnk; K-1,K-1) = kappa(s)(D SCnk; K-1,K-1) = d + 2 for n = 2(d) >= 4 and even k >= 4; kappa(DSCnk; K-1,K-m) = kappa(s)(DSCnk; K-1,K-m) = [(2 )/(d+1)] 1 + 1 with 2 <= m <= d + 2 for n = 2(d) >= 2 and even k >= 4.(c) 2023 Elsevier B.V. All rights reserved.