Largest and smallest eigenvalues of matrices and some Hamiltonian properties of graphs

被引：0
|
作者：
Li, Rao [1 ]
机构：
[1] Univ South Carolina Aiken, Dept Comp Sci Engn & Math, Aiken, SC 29801 USA
来源：
CONTRIBUTIONS TO MATHEMATICS | 2024年 / 10卷
关键词：
matrix; largest eigenvalue; Hamiltonian graph; traceable graph;
D O I：
10.47443/cm.2024.051
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let G ( V, E) be a graph. Define M(G; alpha, /3) : alpha D + /3A, where D and A are the diagonal matrix and adjacency matrix of G , respectively, and alpha , /3 , are real numbers such that ( alpha, /3) 6 (0 , 0) . Using the largest and smallest eigenvalues of M(G; alpha, /3) with alpha >= /3 > 0 , sufficient conditions for the Hamiltonian and traceable graphs are presented.
引用
收藏
页码：34 / 39
页数：6
相关论文
共 42 条
  • [1] On the sum of k largest eigenvalues of graphs and symmetric matrices
    Mohar, Bojan
    JOURNAL OF COMBINATORIAL THEORY SERIES B, 2009, 99 (02) : 306 - 313
  • [2] The largest eigenvalue conditions for Hamiltonian and traceable graphs
    Li, Rao
    DISCRETE MATHEMATICS LETTERS, 2023, 12 : 50 - 53
  • [3] The clique number and some Hamiltonian properties of graphs
    Li, Rao
    CONTRIBUTIONS TO MATHEMATICS, 2021, 4 : 20 - 22
  • [4] Almost sure convergence of the largest and smallest eigenvalues of high-dimensional sample correlation matrices
    Heiny, Johannes
    Mikosch, Thomas
    STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2018, 128 (08) : 2779 - 2815
  • [5] Bounds on Signless Laplacian Eigenvalues of Hamiltonian Graphs
    Andelic, Milica
    Koledin, Tamara
    Stanic, Zoran
    BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, 2021, 52 (03): : 467 - 476
  • [6] Bounds on Signless Laplacian Eigenvalues of Hamiltonian Graphs
    Milica Anđelić
    Tamara Koledin
    Zoran Stanić
    Bulletin of the Brazilian Mathematical Society, New Series, 2021, 52 : 467 - 476
  • [7] The First Zagreb Index and Some Hamiltonian Properties of Graphs
    Li, Rao
    MATHEMATICS, 2024, 12 (24)
  • [8] On the two largest Q-eigenvalues of graphs
    Wang, JianFeng
    Belardo, Francesco
    Huang, QiongXiang
    Borovicanin, Bojana
    DISCRETE MATHEMATICS, 2010, 310 (21) : 2858 - 2866
  • [9] Maximizing the largest eigenvalues of signed unicyclic graphs
    Souri, M.
    Heydari, F.
    Maghasedi, M.
    DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS, 2020, 12 (02)
  • [10] Hamiltonian properties of Toeplitz graphs
    vanDal, R
    Tijssen, G
    Tuza, Z
    vanderVeen, JAA
    Zamfirescu, C
    Zamfirescu, T
    DISCRETE MATHEMATICS, 1996, 159 (1-3) : 69 - 81
12345