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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