改进的拉普拉斯特征值2（无符号）多重性的上界

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2025-09-19 DOI:10.1016/j.laa.2025.09.012

Xueying Li , Ji-Ming Guo , Fenglei Tian , Zhiwen Wang

引用次数: 0

摘要

对于图G，设mL(G,2) (p。， mQ(G,2))表示拉普拉斯函数的多重性。G. Wang et al.(2021)[18]证明了连通图G的mL(G,2)≤c(G)+1，其中c(G)是G的圈数。最近，Zhao and Yu(2025)[19]证明了具有完美匹配的连通图的mQ(G,2)≤c(G)+1。设c2(G)为G的偶圈数，定义为删除G中所有偶圈即可消除的最小边数。对于连通图G，我们证明了ml (G,2)≤c2(G)+1和mq (G,2)≤c2(G)+1，改进了前面两个结果，因为c2(G)≤c(G)。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Improved upper bound of multiplicity of (signless) Laplacian eigenvalue two

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

m_{L} (G, 2) \leq 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

m_{Q} (G, 2) \leq c (G) + 1

for a connected graph with a perfect matching. Let

c_{2} (G)

be the even cyclomatic number of G, defined 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

m_{L} (G, 2) \leq c_{2} (G) + 1 and m_{Q} (G, 2) \leq c_{2} (G) + 1,

improving the two aforementioned results since

c_{2} (G) \leq c (G)

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来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.