The connectivity is an important measurement for the fault tolerance of a network. Let G = (V(G), E(G)) be a connected graph with the vertex set V(G) and edge set E(G). An S‐tree of graph G is a tree T that contains all the vertices in S subject to S⊆V(G). Two S‐trees T and T^′ are internally disjoint if and only if E(T)∩E(T^′) = ∅ and V(T)∩V(T^′) = S. Denote κ_G(S) by the maximum number of internally disjoint S‐trees in graph G. The generalized k‐connectivity is a natural generalization of the classical connectivity, which is defined as κ_r(G) = min{κ_G(S)|S⊆V(G)and|S| = r}. In this paper, we mainly focus on the generalized connectivity of cube‐connected‐cycle CCC_n and hierarchical hypercube HHC_n, which were introduced for massively parallel systems. We show that for n = 2^m + 2(m ≥ 1), κ₄(HHC_n) = m and κ₄(CCC_n) = 2, that is, for any four vertices in CCC_n (or HHC_n), there exist 2 (or m) internally disjoint S‐trees connecting them in CCC_n (or HHC_n).

A supertree is a connected and acyclic hypergraph. Denote by T_m,n,α the set of m‐uniform supertrees of order n with independent number α. Focusing on the spectral radius in T_m,n,α, this present completely determines the hypergraphs with maximum spectral radius among all the supertrees with n vertices and independence number α for [m − 1/mn] ≤ α ≤ n − 1, which extend the results of Lu et al. from tree to uniform supertree. Our techniques are based on the structure properties of supertrees with given independence number and general edge‐moving operation. As a byproduct, we also determine the hypergraphs with minimum signless Laplacian spectral radius in T_m,n,α.