Abstract
Let G be a graph and T a certain connected subgraph of G. The T-structure connectivity κ(G;T) (or resp., T-substructure connectivity κs(G;T)) of G is the minimum number of a set of subgraphs F={T1,T2,…,Tm} (or resp., F={T1′,T2′,…,Tm′}) such that Ti is isomorphic to T (or resp., Ti′ is a connected subgraph of T) for every 1≤i≤m, and F's removal will disconnect G. The twisted hypercube Hn is a new variant of hypercubes with asymptotically optimal diameter introduced by Zhu. In this paper, we will determine both κ(Hn;T) and κs(Hn;T) for T∈{K1,r,Pk}, respectively, where 3≤r≤4 and 1≤k≤n.
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