Connectivity is an important index in evaluating the reliability and fault tolerant ability of interconnection network. However the traditional connectivity is inappropriate for large scale multiprocessor systems. The h-restricted connectivity, as a generalization of traditional connectivity, was proposed to estimate the reliability of interconnection networks more accurately. For an interconnection network G and a positive integer h, the cardinality of a vertex subset F is called the h-restricted connectivity of G, denoted ${\kappa }^h(G)$, if F is the minimum vertex set subject to that $G-F$ is disconnected and $\delta (G-F)\ge h$. In this paper, we investigate the h-restricted connectivity of the generalized hypercube $G(m_r,m_{r-1},\dots ,m_1)$. Specially, we determine that ${\kappa }^h(G(m_r,m_{r-1},\dots ,m_1))=(h+1)\kappa (G(m_r,m_{r-1},\dots ,m_1))-m_{\max }h$ for $1\le h\le \min \{\lfloor \frac{m_r}{2}\rfloor -1,m_{\min }-1,r\}$, where $\kappa (G(m_r,m_{r-1},\dots ,m_1))$ is the connectivity of the generalized hypercube, $m_{\max }=\max \{m_r,m_{r-1},\dots ,m_1\}$ and $m_{\min }=\min \{m_r,m_{r-1},\dots ,m_1\}$.

连接性是评估互连网络的可靠性和容错能力的重要指标。但是，传统的连接性不适用于大型多处理器系统。提出了h限制的连通性，作为传统连通性的概括，以更准确地估计互连网络的可靠性。对于互连网络G和正整数h，顶点子集F的基数称为G的h限制连通性，表示为${\kappa }^H（G）$，如果F是受此约束的最小顶点集$G-F$ 断开连接并 $\delta （G-F）\ge H$。在本文中，我们研究了广义超立方体的h约束连通性$G（{米}_{\mathrm{[R}}，{米}_{\mathrm{[R}-\mathrm{1个}}，\dots ，{米}_{\mathrm{1个}}）$。特别地，我们确定${\kappa }^H（G（{米}_{\mathrm{[R}}，{米}_{\mathrm{[R}-\mathrm{1个}}，\dots ，{米}_{\mathrm{1个}}））=（H+\mathrm{1个}）\kappa （G（{米}_{\mathrm{[R}}，{米}_{\mathrm{[R}-\mathrm{1个}}，\dots ，{米}_{\mathrm{1个}}））-{米}_{\mathrm{最高}}H$ 对于 $\mathrm{1个}\le H\le \mathrm{分}\{\lfloor \frac{{米}_{\mathrm{[R}}}{2}\rfloor -\mathrm{1个}，{米}_{\mathrm{分}}-\mathrm{1个}，\mathrm{[R}\}$，在哪里 $\kappa （G（{米}_{\mathrm{[R}}，{米}_{\mathrm{[R}-\mathrm{1个}}，\dots ，{米}_{\mathrm{1个}}））$ 是广义超立方体的连通性， ${米}_{\mathrm{最高}}=\mathrm{最高}\{{米}_{\mathrm{[R}}，{米}_{\mathrm{[R}-\mathrm{1个}}，\dots ，{米}_{\mathrm{1个}}\}$ 和 ${米}_{\mathrm{分}}=\mathrm{分}\{{米}_{\mathrm{[R}}，{米}_{\mathrm{[R}-\mathrm{1个}}，\dots ，{米}_{\mathrm{1个}}\}$。