Maximum degree and spectral radius of graphs in terms of size

被引：3

作者：

Wang, Zhiwen ^{[1
]}

Guo, Ji-Ming ^{[1
]}

机构：

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

来源：

JOURNAL OF ALGEBRAIC COMBINATORICS | 2024年 / 59卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Spectral radius; Maximum degree; Size; SIGNLESS LAPLACIAN; INDEX;

D O I：

10.1007/s10801-023-01289-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Denote by rho(G) and kappa(G) the spectral radius and the signless Laplacian spectral radius of a graph G, respectively. Let k >= 0 be a fixed integer and G be a graph of size m which is large enough. We show that if rho(G) >= root m - k, then C-4 subset of G or K-1,K-m-k subset of G. Moreover, we prove that if kappa(G) >= m - k + 1, then K-1,K-m-k subset of G. Both these results extend some known results.

引用

页码：213 / 224

页数：12

共 27 条

[1] The signless Laplacian spectral radius of graphs with forbidding linear forests [J].

Chen, Ming-Zhu ;

Liu, A-Ming ;

Zhang, Xiao-Dong .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2020, 591 :25-43

[2] The Maximum Spectral Radius of Graphs Without Friendship Subgraphs [J].

Cioaba, Sebastian ;

Feng, Lihua ;

Tait, Michael ;

Zhang, Xiao-Dong .

ELECTRONIC JOURNAL OF COMBINATORICS, 2020, 27 (04) :1-19

[3] TOWARDS A SPECTRAL THEORY OF GRAPHS BASED ON THE SIGNLESS LAPLACIAN, III [J].

Cvetkovic, Dragos ;

Simic, Slobodan K. .

APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS, 2010, 4 (01) :156-166

[4] TOWARDS A SPECTRAL THEORY OF GRAPHS BASED ON THE SIGNLESS LAPLACIAN, I [J].

Cvetkovic, Dragos ;

Simic, Slobodan K. .

PUBLICATIONS DE L INSTITUT MATHEMATIQUE-BEOGRAD, 2009, 85 (99) :19-33

[5] Towards a spectral theory of graphs based on the signless Laplacian, II [J].

Cvetkovic, Dragos ;

Simic, Slobodan K. .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2010, 432 (09) :2257-2272

[6]

Horn R.A., 1991, Matrix Analysis

[7] Eigenvalues and triangles in graphs [J].

Lin, Huiqiu ;

Ning, Bo ;

Wu, Baoyindureng .

COMBINATORICS PROBABILITY & COMPUTING, 2021, 30 (02) :258-270

[8] Maxima of L-index and Q-index: Graphs with given size and diameter [J].

Lou, Zhenzhen ;

Guo, Ji-Ming ;

Wang, Zhiwen .

DISCRETE MATHEMATICS, 2021, 344 (10)

[9] Some inequalities for the largest eigenvalue of a graph [J].

Nikiforov, V .

COMBINATORICS PROBABILITY & COMPUTING, 2002, 11 (02) :179-189

[10]

Nikiforov V., ARXIV

← 1 2 3 →