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The principal eigenvector to $$\alpha $$α -spectral radius of hypergraphs
Journal of Combinatorial Optimization ( IF 0.9 ) Pub Date : 2020-06-25 , DOI: 10.1007/s10878-020-00617-w
Jing Wang , Liying Kang , Erfang Shan

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.



中文翻译:

超图的$$ \ alpha $$α-谱半径的主要特征向量

对于具有\(rank(H)= r \)的连通超图H,令\(\ mathcal {D}(H)\)\(\ mathcal {A}(H)\)为度的对角张量,H的邻接张量。对于\(0 \文件\阿尔法<1 \) ,该\(\阿尔法\) -spectral半径\(\ RHO _ {\阿尔法}(H)\)ħ被定义为\(\ RHO _ {\阿尔法}(H)= \ max \ {x ^ {T}(\ mathcal {A} _ {\ alpha} x)| x \ in \ mathbf {R} _ {+} ^ {n},\ Vert x \ Vert _ {r} = 1 \} \),其中\(\ mathcal {A} _ {\ alpha}(H)= \ alpha \ mathcal {D}(H)+(1- \ alpha)\ mathcal {A} (H)\)。在本文中,我们给出了与连接的统一超图的\(\ alpha \)谱半径相对应的正单位本征向量项的一些边界。此外,我们获得了与连接的一般超图的\(\ alpha \)谱半径相对应的正单位本征向量项的某些边界。

更新日期:2020-06-25
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