  The lexicographical ordering of hypergraphs via spectral moments is called
the $S$-order of hypergraphs.In this paper, the $S$-order of hypergraphs is
investigated.We characterize the first and last hypergraphs in an $S$-order of
all uniform hypertrees and all linear unicyclic uniformhypergraphs with given
girth, respectively. And we give the last hypergraph in an $S$-order of all
linear unicyclic uniform hypergraphs.
