| 点删除下的图的$A_alpha$特征值的交错性 |
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| 引用本文： | 陈鸿章,李建喜. 点删除下的图的$A_alpha$特征值的交错性[J]. 数学研究及应用, 2022, 42(5): 455-462 |
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| 作者姓名： | 陈鸿章 李建喜 |
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| 作者单位： | 闽南师范大学数学与统计学院, 福建 漳州 363000 |
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| 基金项目： | 国家自然科学基金(Grant No.12171089),福建省自然科学基金(Grant No.2021J02048). |
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| 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$Usubset V$. 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.
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| 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 |
| 收稿时间： | 2021-09-06 |
| 修稿时间： | 2021-12-23 |
Deleting Vertices and Interlacing of $A_alpha$ Eigenvalues of a Graph |
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| Hongzhang CHEN,Jianxi LI. Deleting Vertices and Interlacing of $A_alpha$ Eigenvalues of a Graph[J]. Journal of Mathematical Research with Applications, 2022, 42(5): 455-462 |
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| Authors: | Hongzhang CHEN Jianxi LI |
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| Affiliation: | School of Mathematics and Statistics, Minnan Normal University, Fujian 363000, P. R. China |
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| Abstract: | 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 $Usubseteq V$. 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. |
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| Keywords: | $A_{alpha}$ eigenvalue interlacing inequality independence number cover number Hamiltonian properties spanning tree |
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