文献类型：期刊文献

英文题名：Improved upper bound of multiplicity of (signless) Laplacian eigenvalue two

作者：Li, Xueying[1];Guo, Ji-Ming[1];Tian, Fenglei[2];Wang, Zhiwen[1]

机构：[1]East China Univ Sci & Technol, Sch Math, Shanghai, Peoples R China;[2]Qufu Normal Univ, Sch Management, Rizhao, Shandong, Peoples R China

年份：2026

卷号：728

起止页码：419

外文期刊名：LINEAR ALGEBRA AND ITS APPLICATIONS

收录：;EI(收录号：20253919228104);WOS:【SCI-EXPANDED(收录号:WOS:001583642600001)】；

基金：This work is supported by National Natural Science Foundation of China (Nos. 12171154, 12301438) and the 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：Multiplicity of eigenvalues; Even cycles; Graph transformation

摘要：For a graph G, let m(L)( G, 2)(resp., m(Q)( G, 2)) denote the multiplicity of Laplacian (resp., signless Laplacian) eigenvalue 2 of G. Wang et al. (2021) [18] proved that mL( G, 2)<= c(G)+1 for a connected graph G, where c(G) is the cyclomatic number of G. Very recently, Zhao and Yu (2025) [19] proved that mQ( G, 2)<= c(G)+ 1 for a connected graph with a perfect matching. Let c(2)(G) be the even cyclomatic number of G, defifined as the minimum number of edges whose deletion eliminates all even cycles in G. In this paper, for a connected graph G, we prove that mL( G, 2)<= c(2)(G)+ 1 andmQ( G, 2)<= c(2)(G)+ 1, improving the two aforementioned results since c(2)(G)<= c(G). (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.