Connected Hypergraphs with Small Spectral Radius

2014/02/21 by Linyuan Lü, Lu, Linyuan, Shoudong Man +1 · 3 citations
Mathematics · Computer Science · #Tensor decomposition and applications #Matrix Theory and Algorithms #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.1402.5402

Abstract

In 1970 Smith classified all connected graphs with the 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 the Smith's theorem to r-uniform hypergraphs. We show that the smallest limit point of the spectral radii of connected r-uniform hypergraphs is ρ_r=(r-1)!√[r]4. We discovered a novel method for computing the spectral radius of hypergraphs, and classified all connected r-uniform hypergraphs with spectral radius at most ρ_r.

Cited by

• On the spectral radius of nonregular uniform hypergraphs
• The first few unicyclic and bicyclic hypergraphs with larger spectral radii
• Ordering uniform supertrees by their spectral radii

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