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
收藏
页码：2783 / 2798
页数：16
相关论文
共 31 条
  • [1] On the Ace-spectral radius of connected graphs
    Alhevaz, Abdollah
    Baghipur, Maryam
    Ganie, Hilal Ahmad
    Das, Kinkar Chandra
    [J]. ARS MATHEMATICA CONTEMPORANEA, 2023, 23 (01)
  • [2] Bounds for eigenvalues of the adjacency matrix of a graph
    Bhunia, Pintu
    Bag, Santanu
    Paul, Kallol
    [J]. JOURNAL OF INTERDISCIPLINARY MATHEMATICS, 2019, 22 (04) : 415 - 432
  • [3] On the second largest Aα-eigenvalues of graphs
    Chen, Yuanyuan
    Li, Dan
    Meng, Jixiang
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2019, 580 : 343 - 358
  • [4] Sums of powers of the degrees of a graph
    Cioaba, Sebastian M.
    [J]. DISCRETE MATHEMATICS, 2006, 306 (16) : 1959 - 1964
  • [5] Note on the sum of the smallest and largest eigenvalues of a triangle-free graph
    Csikvari, Peter
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2022, 650 : 92 - 97
  • [6] Cvetkovic D., 2009, An Introduction to the Theory of Graph Spectra
  • [7] Das K. C., 2003, Kragujev. J. Math., V25, P31
  • [8] Maximizing the sum of the squares of the degrees of a graph
    Das, KC
    [J]. DISCRETE MATHEMATICS, 2004, 285 (1-3) : 57 - 66
  • [9] Zagreb indices of graphs
    Das, Kinkar Ch
    Xu, Kexiang
    Nam, Junki
    [J]. FRONTIERS OF MATHEMATICS IN CHINA, 2015, 10 (03) : 567 - 582
  • [10] The spectral radius of graphs on surfaces
    Ellingham, MN
    Zha, XY
    [J]. JOURNAL OF COMBINATORIAL THEORY SERIES B, 2000, 78 (01) : 45 - 56
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