Hypergraphs with Spectral Radius between Two Limit Points
Received:May 23, 2016  Revised:September 22, 2017
Key Word: $r$-uniform hypergraphs   spectral radius   $\alpha$-normal
Fund ProjectL:Supported by the National Natural Science Foundation of China (Grant Nos.11601368; 11401434; 11771322).
 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 Shuhua ZHANG Department of Mathematics, Tianjin University of Finance and Economics, Tianjin 300222, P. R. China
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In this paper, we set $\rho_r=\sqrt[r]{4}$ and $\rho_r'=\beta^{-1/r}$, where $\beta=-\frac{1}{6}\cdot(100+12\cdot \sqrt{69})^{\frac{1}{3}}-\frac{2}{3\cdot(100+12\cdot\sqrt{69})^{\frac{1}{3}}}+\frac{4}{3}\approx 0.2451223338$. We consider connected $r$-uniform hypergraphs with spectral radius between $\rho_r$ and $\rho_r'$ and give a description of such hypergraphs.