  The generalized power of a simple graph $G$, denoted by $G^{k,s}$, is
obtained from $G$ by blowing up each vertex into an $s$-set and each edge into
a $k$-set, where $1 \le s \le \frac{k}{2}$. When $s < \frac{k}{2}$, $G^{k,s}$
is always odd-bipartite. It is known that $G^{k,{k \over 2}}$ is
non-odd-bipartite if and only if $G$ is non-bipartite, and $G^{k,{k \over 2}}$
has the same adjacency (respectively, signless Laplacian) spectral radius as
$G$. In this paper, we prove that, regardless of multiplicities, the
$H$-spectrum of $\A(G^{k,\frac{k}{2}})$ (respectively, $\Q(G^{k,\frac{k}{2}})$)
consists of all eigenvalues of the adjacency matrices (respectively, the
signless Laplacian matrices) of the connected induced subgraphs (respectively,
modified induced subgraphs) of $G$. As a corollary, $G^{k,{k \over 2}}$ has the
same least adjacency (respectively, least signless Laplacian) $H$-eigenvalue as
$G$. We also discuss the limit points of the least adjacency $H$-eigenvalues of
hypergraphs, and construct a sequence of non-odd-bipartite hypergraphs whose
least adjacency $H$-eigenvalues converge to $-\sqrt{2+\sqrt{5}}$.
