  In this paper, the Laplacian characteristic polynomial of uniform hypergraphs
with cut vertices or pendant edges and the Laplacian matching polynomial of
uniform hypergraphs are characterized.The multiplicity of the zero Laplacian
eigenvalue of uniform hypertrees is given, which proves the conjecture in
\cite{zheng2023zero} (The zero eigenvalue of the Laplacian tensor of a uniform
hypergraph, Linear and Multilinear Algebra, (2023)
Doi:10.1080/03081087.2023.2172541).
