On the sum of the first two largest signless Laplacian eigenvalues of a graph

被引：2

作者：

Zhou, Zi-Ming ^{[1
]}

He, Chang-Xiang ^{[1
]}

Shan, Hai-Ying ^{[2
]}

机构：

[1] Univ Shanghai Sci & Technol, Coll Sci, Shanghai, Peoples R China

[2] Tongji Univ, Sch Math Sci, Shanghai, Peoples R China

来源：

DISCRETE MATHEMATICS | 2024年 / 347卷 / 09期

基金：

中国国家自然科学基金;

关键词：

(Signless) Laplacian matrix; (Signless) Laplacian eigenvalues; Sum of (signless) Laplacian eigenvalues;

D O I：

10.1016/j.disc.2024.114035

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a graph G, let S2(G) be the sum of the first two largest signless Laplacian eigenvalues of G, and f (G) = e(G) +3 -S2(G). Oliveira, Lima, Rama and Carvalho conjectured that K+1,n-1 (the star graph with an additional edge) is the unique graph with minimum value of f (G) on n vertices. In this paper, we prove this conjecture, which also confirm a conjecture for the upper bound of S2(G) proposed by Ashraf et al. (c) 2024 Elsevier B.V. All rights reserved.

引用

页数：14

共 17 条

[1]

Amaro B., 2016, Electronic Notes in Discrete Mathematics, V54, P175

[2]

[Anonymous], 2010, On Variants of the Grone-Merris Conjecture

[3] On the extremal values of the second largest Q-eigenvalue [J].

Aouchiche, Mustapha ;

Hansen, Pierre ;

Lucas, Claire .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2011, 435 (10) :2591-2606

[4] On the sum of signless Laplacian eigenvalues of a graph [J].

Ashraf, F. ;

Omidi, G. R. ;

Tayfeh-Rezaie, B. .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2013, 438 (11) :4539-4546

[5]

Brouwer AE, 2012, UNIVERSITEXT, P1, DOI 10.1007/978-1-4614-1939-6

[6] Constraints on Brouwer's Laplacian spectrum conjecture [J].

Cooper, Joshua N. .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2021, 615 :11-27

[7]

Cvetkovic D., 2010, An Introduction to the Theory of Graph Spectra, DOI DOI 10.1017/CBO9780511801518

[8] Upper bounds for the sum of Laplacian eigenvalues of graphs [J].

Du, Zhibin ;

Zhou, Bo .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2012, 436 (09) :3672-3683

[9] ON A THEOREM OF WEYL CONCERNING EIGENVALUES OF LINEAR TRANSFORMATIONS .1. [J].

FAN, K .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1949, 35 (11) :652-655

[10]

Fiedler M., 1986, SPECIAL MATRICES THE

← 1 2 →