Embedded connectivity of recursive networks

Let $G_n$ be an $n$-dimensional recursive network. The $h$-embedded connectivity $ζ_h(G_n)$ (resp. edge-connectivity $η_h(G_n)$) of $G_n$ is the minimum number of vertices (resp. edges) whose removal results in disconnected and each vertex is contained in an $h$-dimensional subnetwork $G_h$. This paper determines $ζ_h$ and $η_h$ for the hypercube $Q_n$ and the star graph $S_n$, and $η_3$ for the bubble-sort network $B_n$.

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