Embedded connectivity of recursive networks

Let Gn be an n-dimensional recursive network. The h-embedded connectivity ζh(Gn) (resp. edge-connectivity ηh(Gn)) of Gn is the minimum number of vertices (resp. edges) whose removal results in disconnected and each vertex is contained in an h-dimensional subnetwork Gh. This paper determines ζh and ηh for the hypercube Qn and the star graph Sn, and η3 for the bubble-sort network Bn.