Structure connectivity and substructure connectivity of wheel networks

Consider a graph Gand its connected subgraph T. The T-structure connectivity kappa(G; T) of Gis the cardinality of a minimum set of subgraphs in G, whose removal disconnects Gand each element in the set is isomorphic to T. The T-substructure connectivity kappa(s)(G; T) of Gis the cardinality of a minimum set of subgraphs in G, whose removal disconnects Gand each element in the set is isomorphic to a connected subgraph of T. In G, the standard connectivity kappa(G) is regarded as a simplification of both kappa(G; T) and kappa(s)(G; T). The wheel network, denoted by CWn, is an attractive interconnected network prototype for multiple CPU systems. In this paper, we determine kappa(CWn; P2k+1)(resp. kappa(s)(CWn; P2k+1)) for n >= 5and k + 1 <= 2n - 4, kappa(CWn; P-2k)(resp. kappa(s)(CWn; P-2k)) for n >= 6 and k <= 2n - 4and a lower bound of kappa(CWn; C-2k)(resp. kappa(s)(CWn; C-2k)) for n >= 6and k <= 2n - 4. (C) 2020 Elsevier B.V. All rights reserved.