Consider a graph G and its connected subgraph T. The T-structure connectivity $\kappa (G;T)$ of G is the cardinality of a minimum set of subgraphs in G, whose removal disconnects G and each element in the set is isomorphic to T. The T-substructure connectivity ${\kappa }^s(G;T)$ of G is the cardinality of a minimum set of subgraphs in G, whose removal disconnects G and 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 $C{W}_n$, is an attractive interconnected network prototype for multiple CPU systems. In this paper, we determine $\kappa (C{W}_n;P_{2k+1})$ (resp. ${\kappa }^s(C{W}_n;P_{2k+1})$) for $n\ge 5$ and $k+1\le 2n-4$, $\kappa (C{W}_n;P_{2k})$ (resp. ${\kappa }^s(C{W}_n;P_{2k})$) for $n\ge 6$ and $k\le 2n-4$ and a lower bound of $\kappa (C{W}_n;C_{2k})$ (resp. ${\kappa }^s(C{W}_n;C_{2k})$) for $n\ge 6$ and $k\le 2n-4$.

考虑图ģ及其连接的子图Ť。该Ť -结构连接$\kappa （G;Ť）$的ģ是最小集合中的子图的基数ģ，其脱除断开ģ和集合中的每个元素是同构Ť。该Ť -substructure连接${\kappa }^s（G;Ť）$的ģ是最小集合中的子图的基数ģ，其脱除断开ģ和集合中的每个元素是同构的连通子Ť。在G中，标准连通性$\kappa （G）$ 被认为是两者的简化 $\kappa （G;Ť）$ 和 ${\kappa }^s（G;Ť）$。车轮网络，用表示$C{\mathrm{w\; ^}}_{ñ}$，是用于多个CPU系统的有吸引力的互连网络原型。在本文中，我们确定$\kappa （C{\mathrm{w\; ^}}_{ñ};P_{2ķ+\mathrm{1个}}）$ （分别 ${\kappa }^s（C{\mathrm{w\; ^}}_{ñ};P_{2ķ+\mathrm{1个}}）$） $ñ\ge 5$ 和 $ķ+\mathrm{1个}\le 2ñ-4$， $\kappa （C{\mathrm{w\; ^}}_{ñ};P_{2ķ}）$ （分别 ${\kappa }^s（C{\mathrm{w\; ^}}_{ñ};P_{2ķ}）$） $ñ\ge 6$ 和 $ķ\le 2ñ-4$ 和下界 $\kappa （C{\mathrm{w\; ^}}_{ñ};C_{2ķ}）$ （分别 ${\kappa }^s（C{\mathrm{w\; ^}}_{ñ};C_{2ķ}）$） $ñ\ge 6$ 和 $ķ\le 2ñ-4$。