论文标题
在均匀加权超图的光谱半径上
On the spectral radius of uniform weighted hypergraph
论文作者
论文摘要
令$ \ mathbb {q} _ {k，n} $是带有$ n $ vertices的连接$ k $ - 均匀加权超图的集合，其中$ k，n \ geq 3 $。 For a hypergraph $G\in \mathbb{Q}_{k,n}$, let $\mathcal{A}(G)$, $\mathcal{L} (G)$ and $\mathcal{Q} (G)$ be its adjacency tensor, Laplacian tensor and signless Laplacian tensor, respectively.研究了$ \ MATHCAL {A}（G）$和$ \ MATHCAL {Q}（G）$的光谱半径。 $ H $ -EIGENVALUE的一些基本属性，$ h^{+} $ - eigenvalue和$ h^{++} $ - eigenvalue的$ \ Mathcal {a}（g）$，$ \ Mathcal {a} $，$ \ nathcal {l}（l}（g）$ and $ \ nathcal $ \ nathcal { $ H $ -EIGENVALUE的几个下限和上限，$ h^{+} $ - eIgenValue和$ h^{++} $ - eigenvalue for $ \ nathcal {a} a}（g）$，$ \ natercal {a}（g）$，$ \ nathcal {l}（l}（l}（g）$ and $ \ natuycal copl最大的$ h^{+} $ - $ \ MATHCAL {l}（g）$的EIGENVALUE和最小的$ h^{+} $ - $ \ MATHCAL {q}（g）$的EigenValue。 $ h $ -eigenValues的$ \ MATHCAL {l}（g）$，$ \ MATHCAL {q}（g）$和$ \ MATHCAL {a}（g）$也是如此。
Let $\mathbb{Q}_{k,n}$ be the set of the connected $k$-uniform weighted hypergraphs with $n$ vertices, where $k,n\geq 3$. For a hypergraph $G\in \mathbb{Q}_{k,n}$, let $\mathcal{A}(G)$, $\mathcal{L} (G)$ and $\mathcal{Q} (G)$ be its adjacency tensor, Laplacian tensor and signless Laplacian tensor, respectively. The spectral radii of $\mathcal{A}(G)$ and $\mathcal{Q} (G)$ are investigated. Some basic properties of the $H$-eigenvalue, the $H^{+}$-eigenvalue and the $H^{++}$-eigenvalue of $\mathcal{A}(G)$, $\mathcal{L} (G)$ and $\mathcal{Q} (G)$ are presented. Several lower and upper bounds of the $H$-eigenvalue, the $H^{+}$-eigenvalue and the $H^{++}$-eigenvalue for $\mathcal{A}(G)$, $\mathcal{L} (G)$ and $\mathcal{Q} (G)$ are established. The largest $H^{+}$-eigenvalue of $\mathcal{L} (G)$ and the smallest $H^{+}$-eigenvalue of $\mathcal{Q} (G)$ are characterized. A relationship among the $H$-eigenvalues of $\mathcal{L} (G)$, $\mathcal{Q} (G)$ and $\mathcal{A} (G)$ is also given.
