Abstract
For a connected hypergraph H with \(rank(H)=r\) , let \(\mathcal {D}(H)\) and \(\mathcal {A}(H)\) be the diagonal tensor of degrees and the adjacency tensor of H, respectively. For \(0 \le \alpha < 1\), the \(\alpha \)-spectral radius \(\rho _{\alpha }(H)\) of H is defined as \(\rho _{\alpha }(H)=\max \{x^{T}(\mathcal {A}_{\alpha }x)|x \in \mathbf {R}_{+}^{n},\Vert x\Vert _{r}=1\}\), where \(\mathcal {A}_{\alpha }(H)=\alpha \mathcal {D}(H)+(1-\alpha )\mathcal {A}(H)\). In this paper, we present some bounds on entries of the positive unit eigenvector corresponding to the \(\alpha \)-spectral radius of connected uniform hypergraphs. Furthermore, we obtain some bounds on entries of the positive unit eigenvector corresponding to the \(\alpha \)-spectral radius of connected general hypergraphs.
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Research was partially supported by the National Nature Science Foundation of China (Grant Numbers 11871329, 11971298).
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Wang, J., Kang, L. & Shan, E. The principal eigenvector to \(\alpha \)-spectral radius of hypergraphs. J Comb Optim 42, 258–275 (2021). https://doi.org/10.1007/s10878-020-00617-w
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DOI: https://doi.org/10.1007/s10878-020-00617-w