Maximizing spectral radius of unoriented Laplacian matrix over bicyclic graphs of a given order

被引：53

作者：

Fan, Yi-Zheng ^{[2
]}

Tam, Bit-Shun ^{[1
]}

Zhou, Jun ^{[2
]}

机构：

[1] Tamkang Univ, Dept Math, Tamsui 251, Taiwan

[2] Anhui Univ, Sch Math & Computat Sci, Hefei 230039, Anhui, Peoples R China

来源：

LINEAR & MULTILINEAR ALGEBRA | 2008年 / 56卷 / 04期

基金：

美国国家科学基金会; 中国国家自然科学基金;

关键词：

unoriented Laplacian matrix; spectral radius; bicyclic graph;

D O I：

10.1080/03081080701306589

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For every integer n >= 4, it is proved that there is a unique graph of order n which maximizes the spectral radius of the unoriented Laplacian matrix over all bicyclic graphs of order n, namely, the graph obtained from the cycle C-4 by first adding a chord and then attaching n-4 pendant edges to one end of the chord.

引用

页码：381 / 397

页数：17

共 50 条

[1] The Laplacian spectral radius of bicyclic graphs with a given girth
Zhai, Mingping
Yu, Guanglong
Shu, Jinlong
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2010, 59 (01) : 376 - 381
[2] The Laplacian spectral radius for bicyclic graphs with given independence number
Wang, Guoping
Guo, Guangquan
ARS COMBINATORIA, 2017, 130 : 275 - 287
[3] THE SIGNLESS LAPLACIAN SPECTRAL RADIUS OF BICYCLIC GRAPHS WITH A GIVEN GIRTH
Zhu, Zhongxun
ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 2011, 22 : 378 - 388
[4] The Signless Laplacian Spectral Radius of Unicyclic and Bicyclic Graphs with a Given Girth
Li, Ke
Wang, Ligong
Zhao, Guopeng
ELECTRONIC JOURNAL OF COMBINATORICS, 2011, 18 (01):
[5] Maximizing the signless Laplacian spectral radius of graphs with given diameter or cut vertices
Wang, Jianfeng
Huang, Qiongxiang
LINEAR & MULTILINEAR ALGEBRA, 2011, 59 (07): : 733 - 744
[6] On the distance Laplacian spectral radius of bicyclic graphs
Xu, Nannan
Yu, Aimei
Hao, Rong-Xia
LINEAR & MULTILINEAR ALGEBRA, 2022, 70 (19): : 4654 - 4674
[7] 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
[8] The Signless Laplacian or Adjacency Spectral Radius of Bicyclic Graphs with Given Number of Cut Edges
Zhen-Mu Hong
Yi-Zheng Fan
Graphs and Combinatorics, 2015, 31 : 1473 - 1485
[9] Graphs with given diameter maximizing the spectral radius
van Dam, E. R.
LINEAR ALGEBRA AND ITS APPLICATIONS, 2007, 426 (2-3) : 454 - 457
[10] The Laplacian spectral radius of graphs with given connectivity
Feng, Lihua
Ilic, Aleksandar
ARS COMBINATORIA, 2012, 104 : 489 - 495

← 1 2 3 4 5 →