2014/12/03 by Linyuan Lü, Lu, Linyuan, Shoudong Man +1
Computer Science · Mathematics · #05C35 #05C50 #05C65 #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms #Spectral Theory (math.SP) #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.1412.1270
openalex publication_date 2014/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In our previous paper, we classified all r-uniform hypergraphs with spectral radius at most (r-1)!√[r]4, which directly generalizes Smith's theorem for the graph case r=2. It is nature to ask the structures of the hypergraphs with spectral radius slightly beyond (r-1)!√[r]4. For r=2, the graphs with spectral radius at most √(2+√(5)) are classified by [\em Brouwer-Neumaier, Linear Algebra Appl., 1989]. Here we consider the r-uniform hypergraphs H with spectral radius at most (r-1)!√[r]2+√(5). We show that H must have a quipus-structure, which is similar to the graphs with spectral radius at most (3)/(2)√(2) [\em Woo-Neumaier, Graphs Combin., 2007].