具有性质 $P^{\ast}$ 的加权邻接矩阵谱半径的指定参数极图
Extremal Graphs with Prescribed Parameters for the Spectral Radius of Weighted Adjacency Matrices with Property $P^{\ast}$
浏览论文内容
中文总结 AI 辅助
本文研究满足性质 $P^{*}$ 的加权邻接矩阵谱半径，刻画了在指定顶点割集、割边数、连通度和独立数条件下达到最大谱半径的极图，发展了统一框架。
中文摘要 AI 辅助
文献中已引入多种基于顶点度的图矩阵，近年来其谱性质的研究引起了广泛关注。受这些进展的启发，本文研究了加权邻接矩阵 $A_f(G)$ 的谱半径，其中函数 $f$ 满足性质 $P^{*}$。更确切地说，我们刻画了在具有指定阶数的顶点割集、恰好具有 $s$ 条割边以及给定顶点连通度和独立数的图类中，使 $A_f(G)$ 的谱半径达到最大的图。我们的结果进一步发展了研究基于度的加权邻接矩阵极值谱性质的统一框架，并将该框架推广到若干具有指定结构参数的图类。
英文摘要
In the literature, several graph matrices based on vertex degrees have been introduced, and the study of their spectral properties has attracted considerable attention in recent years. Motivated by these developments, in this paper, we investigate the spectral radius of the weighted adjacency matrix $A_f(G)$, where the function $f$ satisfies property $P^{*}$. More precisely, we characterize the graphs that attain the maximum spectral radius of $A_f(G)$ among graphs with a vertex cut set of prescribed order, graphs with exactly $s$ cut edges, and graphs with given vertex connectivity and independence number. Our results further develop the unified framework for studying extremal spectral properties of degree-based weighted adjacency matrices and extend this framework to several classes of graphs with prescribed structural parameters.
发表机构
- Manipal Institute of Technology Manipal Academy of Higher Education（马尼帕尔理工学院 马尼帕尔高等教育学院）
机构由 AI 辅助整理，请以论文原文为准。
