Uniform Hypergraphs with α-Spectral Radius at Most That of a Loose Cycle

@misc{cha2026uniform,
  title = {{Uniform Hypergraphs with $α$-Spectral Radius at Most That of a Loose Cycle}},
  author = {Hangxi Cha and Xiaoqi Liu and Haiying Shan},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.24024},
  eprint = {2609.24024},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.24024},
}

TY  - UNPB
TI  - Uniform Hypergraphs with α-Spectral Radius at Most That of a Loose Cycle
AU  - Hangxi Cha
AU  - Xiaoqi Liu
AU  - Haiying Shan
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2609.24024
UR  - https://arxiv.org/abs/2609.24024
AB  - Let k≥ 3 and α∈[0,1), and let λ_k(α) denote the α-spectral radius of a k-uniform loose cycle. Lu and Man classified all connected k-uniform hypergraphs with adjacency spectral radius at most λ_k(0). In this paper, we extend their classification to the α-spectral setting. In particular, for every k≥ 3 and 0<α<1, we prove that λ_k(α) is the smallest limit point of the α-spectral radii of connected k-uniform hypergraphs. Moreover, we give a complete comparison between the α-spectral radius of an arbitrary finite connected k-uniform hypergraph H and that of a loose cycle by determining the sign of ρ_α(H)−λ_k(α). As a consequence, for each fixed 0<α<1, we classify all finite connected k-uniform hypergraphs with α-spectral radius at most λ_k(α).
ER  -