QUADRATIC FORMS ON GRAPHS WITH APPLICATION TO MINIMIZING THE LEAST EIGENVALUE OF SIGNLESS LAPLACIAN OVER BICYCLIC GRAPHS

被引：0
|
作者：
Yu, Gui-Dong [1 ,2 ]
Fan, Yi-Zheng [1 ]
Wang, Yi [1 ]
机构：
[1] Anhui Univ, Sch Math Sci, Hefei 230039, Peoples R China
[2] Anqing Normal Coll, Sch Math & Computat Sci, Anqing 246011, Peoples R China
来源：
ELECTRONIC JOURNAL OF LINEAR ALGEBRA | 2014年 / 27卷
基金：
中国国家自然科学基金;
关键词：
Graph; Bicyclic graph; Quadratic form; Least eigenvalue; Signless Laplacian; UNICYCLIC MIXED GRAPH; SPECTRAL-RADIUS; EIGENVECTORS; CONNECTIVITY; NUMBER; BIPARTITENESS; VERTICES; SPREAD; TREES;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Given a graph and a vector defined on the graph, a quadratic form is defined on the graph depending on its edges. In order to minimize the quadratic form on trees or unicyclic graphs associated with signless Laplacian, the notion of basic edge set of a graph is introduced, and the behavior of the least eigenvalue and the corresponding eigenvectors is investigated. Using these results a characterization of the unique bicyclic graph whose least eigenvalue attains the minimum among all non-bipartite bicyclic graphs of fixed order is obtained.
引用
收藏
页码：213 / 236
页数：24
相关论文
共 50 条
  • [21] THE LEAST EIGENVALUE OF THE SIGNLESS LAPLACIAN OF NON-BIPARTITE UNICYCLIC GRAPHS WITH K PENDANT VERTICES
    Liu, Ruifang
    Wan, Haixia
    Yuan, Jinjiang
    Jia, Huicai
    ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 2013, 26 : 333 - 344
  • [22] The least eigenvalue of the signless Laplacian of the complements of trees
    Li, Shuchao
    Wang, Shujing
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2012, 436 (07) : 2398 - 2405
  • [23] Balancedness and the least eigenvalue of Laplacian of signed graphs
    Belardo, Francesco
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2014, 446 : 133 - 147
  • [24] THE SMALLEST SIGNLESS LAPLACIAN EIGENVALUE OF GRAPHS UNDER PERTURBATION
    He, Chang-Xiang
    Pan, Hao
    ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 2012, 23 : 473 - 482
  • [25] On the Largest Eigenvalue of Signless Laplacian Matrix of Halin Graphs
    Zhu, Xiaoxin
    Wu, Yajuan
    PROCEEDINGS OF THE 2010 INTERNATIONAL CONFERENCE ON APPLICATION OF MATHEMATICS AND PHYSICS, VOL 2: ADVANCES ON APPLIED MATHEMATICS AND COMPUTATION MATHEMATICS, 2010, : 113 - 116
  • [26] The least eigenvalue of graphs with given connectivity
    Ye, Miao-Lin
    Fan, Yi-Zheng
    Liang, Dong
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2009, 430 (04) : 1375 - 1379
  • [27] On the signless Laplacian index and radius of graphs
    Liu, Huiqing
    Lu, Mei
    Zhang, Shunzhe
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2017, 519 : 327 - 342
  • [28] On the least signless Laplacian eigenvalue of non-bipartite unicyclic graphs with both given order and diameter
    Guo, Shu-Guang
    Xu, Meiling
    Yu, Guanglong
    ARS COMBINATORIA, 2014, 114 : 385 - 395
  • [29] Distance signless Laplacian eigenvalues of graphs
    Das, Kinkar Chandra
    Lin, Huiqiu
    Guo, Jiming
    FRONTIERS OF MATHEMATICS IN CHINA, 2019, 14 (04) : 693 - 713
  • [30] The Signless Laplacian or Adjacency Spectral Radius of Bicyclic Graphs with Given Number of Cut Edges
    Hong, Zhen-Mu
    Fan, Yi-Zheng
    GRAPHS AND COMBINATORICS, 2015, 31 (05) : 1473 - 1485
12345