  In this paper, we show that the largest signless Laplacian H-eigenvalue of a
connected $k$-uniform hypergraph $G$, where $k \ge 3$, reaches its upper bound
$2\Delta(G)$, where $\Delta(G)$ is the largest degree of $G$, if and only if
$G$ is regular. Thus the largest Laplacian H-eigenvalue of $G$, reaches the
same upper bound, if and only if $G$ is regular and odd-bipartite. We show that
an $s$-cycle $G$, as a $k$-uniform hypergraph, where $1 \le s \le k-1$, is
regular if and only if there is a positive integer $q$ such that $k=q(k-s)$. We
show that an even-uniform $s$-path and an even-uniform non-regular $s$-cycle
are always odd-bipartite. We prove that a regular $s$-cycle $G$ with $k=q(k-s)$
is odd-bipartite if and only if $m$ is a multiple of $2^{t_0}$, where $m$ is
the number of edges in $G$, and $q = 2^{t_0}(2l_0+1)$ for some integers $t_0$
and $l_0$. We identify the value of the largest signless Laplacian H-eigenvalue
of an $s$-cycle $G$ in all possible cases. When $G$ is odd-bipartite, this is
also its largest Laplacian H-eigenvalue. We introduce supervertices for
hypergraphs, and show the components of a Laplacian H-eigenvector of an
odd-uniform hypergraph are equal if such components corresponds vertices in the
same supervertex, and the corresponding Laplacian H-eigenvalue is not equal to
the degree of the supervertex. Using this property, we show that the largest
Laplacian H-eigenvalue of an odd-uniform generalized loose $s$-cycle $G$ is
equal to $\Delta(G)=2$. We also show that the largest Laplacian H-eigenvalue of
a $k$-uniform tight $s$-cycle $G$ is not less than $\Delta(G)+1$, if the number
of vertices is even and $k=4l+3$ for some nonnegative integer $l$.
