AI 中文总结
研究给定阶数\(n\)和解离数\(\psi\)的连通图的最小谱半径，对于\(\psi=n - k\)（\(k\geq4\)固定且\(n\)足够大），建立上下界并证明极值图所属类别。
AI 中文摘要
图中的解离集是诱导出最大度至多为\(1\)的子图的顶点子集，是独立集概念的自然推广。图的解离数定义为解离集的最大基数。本文研究具有给定阶数\(n\)和给定解离数\(\psi\)的连通图的最小谱半径。对于\(\psi=n - k\)（\(k\geq4\)固定且\(n\)足够大），我们建立了该最小谱半径的上下界，并证明极值图必须属于特定的图类。
英文摘要
A dissociation set in a graph is a subset of vertices that induces a subgraph of maximum degree at most one, which is a natural generalization of the notion of an independent set. The dissociation number of a graph is defined as the maximum cardinality of a dissociation set. This paper studies the minimum spectral radius of connected graphs with a given order $n$ and a given dissociation number $ψ$. For $ψ=n-k$ with $k\ge 4$ fixed and $n$ sufficiently large, we establish both upper and lower bounds for this minimum spectral radius and prove the extremal graphs must belong to a specific graph class.
