Hypergraphs with Spectral Radius at most $\sqrt[r]{2+\sqrt{5}}$
Hypergraphs with Spectral Radius at most $\sqrt[r]{2+\sqrt{5}}$

DOI：

 作者 单位 E-mail 满守东 天津财经大学 manshoudong@163.com 陆临渊 University of South Carolina, Columbia, SC 29208, USA

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 Brouwer-Neumaier, 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 quipus-structure, which is similar to the graphs with spectral radius at most $\frac{3}{2}\sqrt{2}$ [{\em Woo-Neumaier, Graphs Combin. 2007}].
查看/发表评论  下载PDF阅读器