Sharp upper bounds on the second largest signless Laplacian eigenvalues of connected graphs

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2025-07-07 DOI:10.1016/j.laa.2025.07.004

Shu-Guang Guo, Rong Zhang

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引用次数: 0

Abstract

Let G be a connected graph with n vertices and m edges, and

q_{2} (G)

denote the second largest signless Laplacian eigenvalue of G. A conjecture, due to Cvetković et al. (2007), asserts that

q_{2} (G) \leq n - 6 + (2 m + 8) / n

with equality if and only if G is the complete bipartite graph

K_{2, n - 2}

. In this paper, we give sharp upper bounds on

q_{2} (G)

for a connected (minimally 2-connected) graph with given size. Employing the upper bounds, we prove that the conjecture holds for a connected bipartite graph, for a minimally 2-connected graph and for a connected graph with

m \neq 2 n - 5

and

2 n - 6

, respectively.

查看原文本刊更多论文

连通图的第二大无符号拉普拉斯特征值的明显上界

设G是一个有n个顶点和m条边的连通图，q2(G)表示G的第二大无符号拉普拉斯特征值。cvetkoviki et al.（2007）的一个猜想断言，当且仅当G是完全二部图K2，n - 2时，q2(G)≤n - 6+(2m+8)/n相等。本文给出了给定大小的连通（最小2连通）图的q2(G)的明显上界。利用上界证明了该猜想分别适用于连通二部图、最小2连通图和m≠2n−5和2n−6的连通图。

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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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.