文献类型：期刊文献

英文题名：Multiplicity of graph Hermitian eigenvalues

作者：Chen, Qian-Qian[1];Wang, Zhiwen[2]

机构：[1]Yancheng Teachers Univ, Sch Math & Stat, Yancheng 224002, Peoples R China;[2]East China Univ Sci & Technol, Sch Math, Shanghai 200237, Peoples R China

年份：2026

卷号：736

起止页码：175

外文期刊名：LINEAR ALGEBRA AND ITS APPLICATIONS

收录：;EI(收录号：20260620028307);WOS:【SCI-EXPANDED(收录号:WOS:001687570600001)】；

基金：star This work is supported by National Natural Science Foundation of China (No. 12301438) , Chenguang Program of Shanghai Education Development Foundation and Shanghai Municipal Education Commission (No. 23CGA37) and Youth Innovation Team Project of Shandong Province Universities (No. 2023KJ353) .

语种：英文

外文关键词：Graph; Hermitian matrix; Eigenvalue; Multiplicity

摘要：Let G be a graph with vertex set {1, 2, ... , n}, and H be the graph obtained by attaching one pendant path of length k(i) at vertex i (i = 1, ... , r, 1 <= r <= n). Given an Hermitian matrix B whose graph is H, denote by m(B)(H, lambda) the multiplicity of an eigenvalue lambda of B. It is proved by da Fonseca (2005) that m(B)(H,lambda) <= n, and then Bu et al. (2014) provided a characterization to extremal graphs with the equality. The extremal graphs show that G congruent to nK1, i.e., His disconnected. In this note, we characterize all connected graphs attaining the upper bound of m(B)(H,lambda) <= n-1. All graphs H with m(B)(H, lambda) = n-1 are surely determined. In terms of the number of quasi-pendant vertices, we give a new upper bound of eigenvalue multiplicity m(B)(G, lambda) for any Hermitian matrix B(G) on a general graph G. Moreover, we explore the relationship between the multiplicities of Hermitian eigenvalues of a graph and its reduced graph. Since adjacency and (signless) Laplacian matrix are Hermitian matrix, these results extend several recent works. (c) 2026 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.