点删除下的图的$A_\alpha$特征值的交错性

Deleting Vertices and Interlacing of $A_\alpha$ Eigenvalues of a Graph

中文关键词:  $A_\alpha$特征值  交错不等式  独立数  点覆盖数  哈密尔顿性  支撑树

英文关键词:$A_{\alpha}$ eigenvalue  interlacing inequality  independence number  cover number  Hamiltonian properties  spanning tree

中文摘要:

      设$G$为具有顶点集$V$, 边集$E$的简单图, 本文给出了图$G$与其子图$G-U$的$A_\alpha$特征值的交错不等式, 其中$U\subset V$. 作为应用, 我们利用该交错不等式导出了一些关于图的独立数, 点覆盖数, 哈密尔顿性及支撑数的$A_\alpha$ 谱条件.

英文摘要:

      Let $G$ be simple graph with vertex set $V$ and edge set $E$. In this paper, we establish an interlacing inequality between the $A_{\alpha}$ eigenvalues of $G$ and its subgraph $G-U$, where $U\subseteq V$. Moreover, as an application, this interlacing property can be used to deduce some $A_{\alpha}$ spectral conditions concerning the independence number, cover number, Hamiltonian property and spanning tree of a graph, respectively.