Abstract
For a connected k-uniform hypergraph H, let \({\mathcal {A}}_\alpha (H)=\alpha {\mathcal {D}}(H)+(1-\alpha ){\mathcal {A}}(H)\), where \({\mathcal {A}}(H)\)(resp. \({\mathcal {D}}(H)\)) is its adjacency (resp. degree) tensor and \(0\le \alpha <1\). We call the least real eigenvalue of \({\mathcal {A}}_\alpha (H)\) having a real eigenvector as \(\alpha \)-least eigenvalue of H. In this paper, we obtain some properties on \(\alpha \)-least eigenvalue of H. As their applications, the extremal hypergraphs whose \(\alpha \)-least eigenvalue attaining minimum are characterized among some classes of hypergraphs.
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Communicated by Carlos Hoppen.
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This work is supported by the Special Fund for Basic Scientific Research of Central Colleges, South-Central University for Nationalities (CZZ21014)
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Zhou, J., Zhu, Z. Some properties on \(\alpha \)-least eigenvalue of uniform hypergraphs and their applications. Comp. Appl. Math. 41, 94 (2022). https://doi.org/10.1007/s40314-022-01797-3
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DOI: https://doi.org/10.1007/s40314-022-01797-3