文献类型：期刊文献

英文题名：Upper bounds for the multiplicity of Laplacian eigenvalues of graphs

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

机构：[1]East China Univ Sci & Technol, Sch Math, Shanghai 200237, Peoples R China

年份：2026

卷号：349

期号：9

外文期刊名：DISCRETE MATHEMATICS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:001742420100001)】；

基金：star This work is supported by National Natural Science Foundation of China (Nos. 12171154, 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：Laplacian eigenvalue; Multiplicity; Upper bound

摘要：For a graph G, the multiplicity of lambda as a Laplacian eigenvalue of G is denoted by mG(lambda). In this paper, we prove that for any tree T =/ K1,n-1, where K1,n-1 is a star with n vertices, if lambda =/ 1, then mT(lambda) <= q(T)-1, where q(T) is the number of quasi-pendant vertices of T. Moreover, we characterize the trees for which equality holds. Furthermore, for any connected graph G with n vertices and m edges, if lambda =/ 1, then mG(lambda) <= 2c(G) + q(G), where c(G) = m-n + 1 is the cyclomatic number of G, and the equality holds if and only if G is either a star K1,n-1 or a cycle Cnwith lambda is an element of/{0, 4}. In particular, we show that mG(1) <= 2c(G)+p(G), where p(G) is the number of pendant vertices of G, and the equality holds if and only if G = Cnand 6|n. Our results extend several known results. (c) 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.