Hypergraphs with Spectral Radius at most $\sqrt[r]{2+\sqrt{5}}$ 
Received:February 06, 2018 Revised:February 06, 2018 
Key Word:
$r$uniform hypergraphs, spectral radius, $\alpha$normal

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Abstract: 
In our previous paper, we classified all $r$uniform hypergraphs with spectral radius at most $\sqrt[r]{4}$, which directly generalizes Smith's theorem for the graph case $r=2$. It is natural to investigate the structures of the hypergraphs with spectral radius slightly beyond $\sqrt[r]{4}$. For $r=2$, the graphs with spectral radius at most $\sqrt{2+\sqrt{5}}$ are classified by [{\em BrouwerNeumaier, Linear Algebra Appl., 1989}]. Here we consider the $r$uniform hypergraphs $H$ with spectral radius at most $\sqrt[r]{2+\sqrt{5}}$. We show that $H$ must have a quipusstructure, which is similar
to the graphs with spectral radius at most $\frac{3}{2}\sqrt{2}$ [{\em WooNeumaier, Graphs Combin. 2007}]. 
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