Bounds for Aα-eigenvalues

被引：0

作者：

da Silva Jr, Joao Domingos Gomes ^{[1
]}

Oliveira, Carla Silva ^{[2
]}

da Costa, Liliana Manuela G. C. ^{[3
]}

机构：

[1] Ctr Fed Educ Tecnol Rio De Janeiro, Dept Engn Prod, Rio De Janeiro, Brazil

[2] Escola Nacl Ciencias Estat, Dept Matemat, Rio De Janeiro, Brazil

[3] Colegio Pedro II, Dept Matemat, Rio De Janeiro, Brazil

来源：

RAIRO-OPERATIONS RESEARCH | 2023年 / 57卷 / 05期

关键词：

A(alpha)-matrix; A(alpha)-eigenvalues; bounds; SPECTRAL-RADIUS; A(ALPHA)-SPECTRAL RADIUS; ZAGREB INDEXES; EIGENVALUES; SUM;

D O I：

10.1051/ro/2023144

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

Let G be a graph with adjacency matrix A(G) and degree diagonal matrix D(G). In 2017, Nikiforov (V. Nikiforov, Appl. Anal. Discret. Math. 11 (2017) 81-107.) defined the matrix A alpha(G), as a convex combination of A(G) and D(G), the following way, A(alpha)(G) = alpha A(G) + (1 - alpha)D(G) where alpha is an element of [0,1]. In this paper we present some new upper and lower bounds for the largest, second largest and the smallest eigenvalue of A(alpha)-matrix. Moreover, extremal graphs attaining some of these bounds are characterized.

引用

页码：2783 / 2798

页数：16

共 31 条

[1] On the Ace-spectral radius of connected graphs [J].

Alhevaz, Abdollah ;

Baghipur, Maryam ;

Ganie, Hilal Ahmad ;

Das, Kinkar Chandra .

ARS MATHEMATICA CONTEMPORANEA, 2023, 23 (01)

[2] Bounds for eigenvalues of the adjacency matrix of a graph [J].

Bhunia, Pintu ;

Bag, Santanu ;

Paul, Kallol .

JOURNAL OF INTERDISCIPLINARY MATHEMATICS, 2019, 22 (04) :415-432

[3] On the second largest Aα-eigenvalues of graphs [J].

Chen, Yuanyuan ;

Li, Dan ;

Meng, Jixiang .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2019, 580 :343-358

[4] Sums of powers of the degrees of a graph [J].

Cioaba, Sebastian M. .

DISCRETE MATHEMATICS, 2006, 306 (16) :1959-1964

[5] Note on the sum of the smallest and largest eigenvalues of a triangle-free graph [J].

Csikvari, Peter .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2022, 650 :92-97

[6]

Cvetkovic D., 2009, An introduction to the theory of graph spectra

[7]

Das, 2003, KRAGUJEV J MATH, V25, P19

[8] Maximizing the sum of the squares of the degrees of a graph [J].

Das, KC .

DISCRETE MATHEMATICS, 2004, 285 (1-3) :57-66

[9] Zagreb indices of graphs [J].

Das, Kinkar Ch ;

Xu, Kexiang ;

Nam, Junki .

FRONTIERS OF MATHEMATICS IN CHINA, 2015, 10 (03) :567-582

[10] The spectral radius of graphs on surfaces [J].

Ellingham, MN ;

Zha, XY .

JOURNAL OF COMBINATORIAL THEORY SERIES B, 2000, 78 (01) :45-56

← 1 2 3 4 →