Connected hypergraphs with small spectral radius

Linyuan Lu, Shoudong Man
2016 Linear Algebra and its Applications  
In 1970 Smith classified all connected graphs with spectral radius at most 2. Here the spectral radius of a graph is the largest eigenvalue of its adjacency matrix. Recently, the definition of spectral radius has been extended to r-uniform hypergraphs. In this paper, we generalize Smith's theorem to r-uniform hypergraphs. We show that the smallest limit point of the spectral radii of connected r-uniform hypergraphs is ρr = r √ 4. We discovered a novel method for computing the spectral radius of
more » ... hypergraphs, and classified all connected r-uniform hypergraphs with spectral radius at most ρr.
doi:10.1016/j.laa.2016.07.013 fatcat:tpenelmew5fxjiwd3yurvhjy24