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In our previous paper, we classified all $r$-uniform hypergraphs withspectral radius at most $(r-1)!\sqrt[r]{4}$, which directly generalizes Smith'stheorem for the graph case $r=2$. It is nature to ask the structures of thehypergraphs with spectral radius slightly beyond $(r-1)!\sqrt[r]{4}$. For$r=2$, the graphs with spectral radius at most $\sqrt{2+\sqrt{5}}$ areclassified by [{\em Brouwer-Neumaier, Linear Algebra Appl., 1989}]. Here weconsider the $r$-uniform hypergraphs $H$ with spectral radius at most$(r-1)!\sqrt[r]{2+\sqrt{5}}$. We show that $H$ must have a quipus-structure,which is similar to the graphs with spectral radius at most$\frac{3}{2}\sqrt{2}$ [{\em Woo-Neumaier, Graphs Combin., 2007}].

Hypergraphs with Spectral Radius at most $(r-1)!\sqrt[r]{2+\sqrt{5}}$