Structure Fault Tolerance of WK-recursive Networks

The WK-recursive networks K(d, t) have many good properties, which are a kind of recursively constructed interconnection networks. In this paper, we will study two kinds of network connectivities, which are called H-structure-connectivity and H-substructure- connectivity respectively. These two kinds of network connectivities measure a network's reliability based on structure faults. Let F be a set of subgraphs of graph G, where the deletion of all the elements of F from G makes G disconnected or trivial. Then F is an H-structure-cut if each element in F is isomorphic to H, where H is a subgraph of G. The H-structure-connectivity of G is the minimum cardinality of all the H-structure-cuts of G, denoted by kappa(G; H). If each element of F is isomorphic to a connected subgraph of H, F is an H-substructure-cut of G. The H-substructure-connectivity of G is the minimum cardinality of all H-substructure-cuts of G, denoted by kappa(s)(G; H). We study kappa(K(d, t); H) and kappa(s)(K(d, t); H) of the WK-recursive networks, where H is an element of{K-1, K-1,K-N, C-4} and N is an element of{1, 2, 3}. (C) 2022 Elsevier B.V. All rights reserved.