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

Lexicographical ordering of hypergraphs via spectral moment