On the Laplacian integral tricyclic graphs

被引：8
|
作者：
Huang, Xueyi [1 ]
Huang, Qiongxiang [1 ]
Wen, Fei [1 ]
机构：
[1] Xinjiang Univ, Coll Math & Syst Sci, Urumqi, Peoples R China
来源：
LINEAR & MULTILINEAR ALGEBRA | 2015年 / 63卷 / 07期
关键词：
tricyclic graph; Laplacian integral graph; algebraic connectivity; 05C50; R-PARTITE GRAPHS; ALGEBRAIC CONNECTIVITY; EIGENVALUES; MATRICES; SPECTRUM;
D O I：
10.1080/03081087.2014.936436
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A graph is called Laplacian integral if all its Laplacian eigenvalues are integers. In this paper, we give an edge subdividing theorem for Laplacian eigenvalues of a graph (Theorem 2.1) and characterize a class of k-cyclic graphs whose algebraic connectivity is less than one. Using these results, we determine all the Laplacian integral tricyclic graphs. Furthermore, we show that all the Laplacian integral tricyclic graphs are determined by their Laplacian spectra.
引用
收藏
页码：1356 / 1371
页数：16
相关论文
共 50 条
  • [31] On conjectures involving second largest signless Laplacian eigenvalue of graphs
    Das, Kinkar Ch.
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2010, 432 (11) : 3018 - 3029
  • [32] On the Laplacian spectral ratio of connected graphs
    You, Zhifu
    Liu, Bolian
    APPLIED MATHEMATICS LETTERS, 2012, 25 (10) : 1245 - 1250
  • [33] The signless Laplacian spectral radius of tricyclic graphs and trees with k pendant vertices
    Li, Ke
    Wang, Ligong
    Zhao, Guopeng
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2011, 435 (04) : 811 - 822
  • [34] Distance Laplacian spectra of graphs: A survey
    Rather, Bilal Ahmad
    Aouchiche, Mustapha
    DISCRETE APPLIED MATHEMATICS, 2025, 361 : 136 - 195
  • [35] Toughness and normalized Laplacian eigenvalues of graphs
    Huang, Xueyi
    Das, Kinkar Chandra
    Zhu, Shunlai
    APPLIED MATHEMATICS AND COMPUTATION, 2022, 425
  • [36] Edge perturbation on graphs with clusters: Adjacency, Laplacian and signless Laplacian eigenvalues
    Cardoso, Domingos M.
    Rojo, Oscar
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2017, 512 : 113 - 128
  • [37] Graphs with Maximum Laplacian-Energy-Like Invariant and Incidence Energy
    de Freitas, Maria Aguieras A.
    Gutman, Ivan
    Robbiano, Maria
    MATCH-COMMUNICATIONS IN MATHEMATICAL AND IN COMPUTER CHEMISTRY, 2016, 75 (02) : 331 - 342
  • [38] On Laplacian integrability of comaximal graphs of commutative rings
    Rather, Bilal Ahmad
    Aouchiche, Mustapha
    Imran, Muhammed
    INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2024, 55 (01) : 310 - 324
  • [39] New bounds on the Laplacian spectral ratio of connected graphs
    Lin, Zhen
    Cai, Min
    Wang, Jiajia
    CZECHOSLOVAK MATHEMATICAL JOURNAL, 2024, 74 (04) : 1207 - 1220
  • [40] The Laplacian spread of line graphs
    Zhang, Jianbin
    Wu, Yinglin
    Li, Jianping
    DISCRETE MATHEMATICS, 2023, 346 (01)
12345