The Sharp Upper Bounds on the Aα-Spectral Radius of C4-Free Graphs and Halin Graphs

被引：0

作者：

Guo, Shu-Guang ^{[1
]}

Zhang, Rong ^{[1
]}

机构：

[1] Yancheng Teachers Univ, Sch Math & Stat, Yancheng 224002, Jiangsu, Peoples R China

来源：

GRAPHS AND COMBINATORICS | 2022年 / 38卷 / 01期

基金：

中国国家自然科学基金;

关键词：

C-4-Free graph; Halin graph; A(alpha)-Spectral; Upper bound; EXTREMAL ALPHA-INDEX; SPECTRAL-RADIUS; MAXIMA;

D O I：

10.1007/s00373-021-02429-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a simple undirected graph. For any real number alpha is an element of [0, 1], Nikiforov defined the A(alpha)-matrix of G as A(alpha)(G) = alpha D(G) + (1 - alpha)A(G), where A(G) and D(G) are the adjacency matrix and the degree diagonal matrix of G respectively. The largest eigenvalue of A(alpha)(G) is called the Aa-spectral radius of G. In this paper, we give sharp upper bounds on the Aa-spectral radius of C-4-free graphs and Halin graphs for alpha is an element of [1/2, 1) respectively.

引用

页数：13

共 26 条

[11] MERGING THE A- AND Q-SPECTRAL THEORIES [J].

Nikiforov, V. .

APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS, 2017, 11 (01) :81-107

[12]

Nikiforov V., 2011, Surveys in Combinatorics., V392, P141

[13] On the α-index of graphs with pendent paths [J].

Nikiforov, Vladimir ;

Rojo, Oscar .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2018, 550 :87-104

[14] On the Aα-spectra of trees [J].

Nikiforov, Vladimir ;

Pasten, Germain ;

Rojo, Oscar ;

Soto, Ricardo L. .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2017, 520 :286-305

[15] Maxima of the Q-index: Forbidden even cycles [J].

Nikiforov, Vladimir ;

Yuan, Xiying .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2015, 471 :636-653

[16]

Rojo O, 2020, ELECTRON J LINEAR AL, V36, P38

[17]

Shu J.L., 2000, Chinese Ann. Math. Ser., V21, P677

[18]

Stanic Z., 2015, London Mathematical Society Lecture Note Series, DOI DOI 10.1017/CBO9781316341308

[19]

Stevanovic D., 2015, Spectral Radius of Graphs

[20] The extremal α-index of graphs with no 4-cycle and 5-cycle [J].

Tian, Gui-Xian ;

Chen, Ya-Xue ;

Cui, Shu-Yu .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2021, 619 :160-175

← 1 2 3 →