Hypergraphs with Spectral Radius at Most $\sqrt[r]{2+\sqrt{5}}$
Received:February 06, 2018  Revised:December 11, 2018
Key Word: $r$-uniform hypergraphs   spectral radius   $\alpha$-normal
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant No.11601368).
 Author Name Affiliation Shoudong MAN Department of Mathematics, Tianjin University of Finance and Economics, Tianjin 300222, P. R. China Linyuan LU Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA
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In this paper, we consider the $r$-uniform hypergraphs $H$ with spectral radius at most $\sqrt[r]{2+\sqrt{5}}$. We show that $H$ must have a quipus-structure, which is similar to the graphs with spectral radius at most $\frac{3}{2}\sqrt{2}$ [Woo-Neumaier, Graphs Combin. 2007].