  For a $k$-uniform hypergraph $H$, we obtain some trace formulas for the
Laplacian tensor of $H$, which imply that $\sum_{i=1}^nd_i^s$ ($s=1,\ldots,k$)
is determined by the Laplacian spectrum of $H$, where $d_1,\ldots,d_n$ is the
degree sequence of $H$. Using trace formulas for the Laplacian tensor, we
obtain expressions for some coefficients of the Laplacian polynomial of a
regular hypergraph. We give some spectral characterizations of odd-bipartite
hypergraphs, and give a partial answer to a question posed by Shao et al
\cite{ShaoShanWu}. We also give some spectral properties of power hypergraphs,
and show that a conjecture posed by Hu et al \cite{HuQiShao} holds under
certain conditons.
