186 research outputs found

    Connected Hypergraphs with Small Spectral Radius

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    In 1970 Smith classified all connected graphs with the spectral radius at most 22. 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 rr-uniform hypergraphs. In this paper, we generalize the Smith's theorem to rr-uniform hypergraphs. We show that the smallest limit point of the spectral radii of connected rr-uniform hypergraphs is ρr=(rβˆ’1)!4r\rho_r=(r-1)!\sqrt[r]{4}. We discovered a novel method for computing the spectral radius of hypergraphs, and classified all connected rr-uniform hypergraphs with spectral radius at most ρr\rho_r.Comment: 20 pages, fixed a missing class in theorem 2 and other small typo
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