倒距离矩阵的谱半径(英文)

本文刻画了在分别具有给定点连通度、边连通度、色数和独立数的n阶图中具有最大倒距离矩阵谱半径的图.     

倒距离矩阵的谱半径(英文)北大核心CSCD

本文刻画了在分别具有给定点连通度、边连通度、色数和独立数的n阶图中具有最大倒距离矩阵谱半径的图.     

图的点覆盖数与其Laplace谱半径

本文讨论图的点覆盖数与图的 Laplace谱半径的关系 ,利用特征向量的技巧得到由图的 L aplace谱半径所确定的关于图的点覆盖数的紧的界     

有向图的Laplace谱半径

Laplace矩阵的谱半径一直是近年来谱图理论的研究热点.本文主要讨论有向图Laplace矩阵的谱半径,用顶点的出度和公共邻域数给出了谱半径上界,用图的最大出度给出了一些特殊图类谱半径的下界.     

n阶三圈图的补图的谱半径

三圈图是边数等于顶点数加2的简单连通图.在所有n阶三圈图的补图中,哪一个的谱半径最大?文中给出了n阶三圈图的补图的谱半径的上界,并刻画了唯一的达到该上界的图.     

不含三圈的k圈图的拟拉普拉斯和拉普拉斯谱半径

k圈图是边数等于顶点数加k-1的简单连通图.文中确定了不含三圈的k圈图的拟拉普拉斯谱半径的上界,并刻画了达到该上界的极图.此外,文中确定了拟拉普拉斯谱半径排在前五位的不含三圈的单圈图,排在前八位的不含三圈的双圈图.最后说明文中所得结论对不含三圈的k圈图的拉普拉斯谱半径也成立.     

一些极值图问题的谱条件综述（英文）

这篇综述分为两个方面.首先,我们总结了图论中的Turan型问题的谱极值结论的最新进展.更准确地说,关于各种图的邻接谱半径和无符号拉普拉斯谱半径,我们总结了它们的谱版本的Turán型函数.例如,完全图、色数至少为3的一般图、完全二部图、奇圈、偶圈、色临界图和相交三角形图.第二个目标是总结一些最近的关于图性质的谱条件.通过一种统一的方法,基于邻接谱半径和无符号拉普拉斯谱半径,我们给出了一些充分条件,使得该图成为哈密顿图、k-哈密顿图、k-边哈密顿图、可迹图、k-路径可覆盖图、k-连通图、k-边连通图、哈密顿连通图、完美匹配图和β-亏量图.     

非正则图的谱半径

讨论了由D.Stevanovi′c提出的给定顶点数n 和最大度?的非正则图的谱半径的上界,并给出了一些新的由?表示的谱半径的界.     

给定最大度的单圈偶图的谱半径

单圈偶图是边数等于顶点数的简单连通偶图.Δ（G）表示图G的最大度.文中给出了最大度为Δ(≥ⁿ⁺¹/2)的n阶单圈偶图的谱半径的上界,并刻画了达到该上界的图.文中还证明了当Δ（G）≥[（2n+1）/3]+1时,n（≥8）阶单圈偶图G的谱半径随着最大度的递增而严格递增,并在此基础上给出了谱半径排在前17位的n（≥16）阶单圈偶图.     

给定染色数的无符号Laplace谱半径

设Gkn(k≥2)为n阶的染色数为k的连通图的集合.本文确定了Gkn中具有极大无符号Laplace谱半径的图,即k=2时为完全二部图,k≥3时为Turn图.本文也讨论了Gkn中的具有极小无符号Laplace谱半径的图,对k≤3的情形给出了此类图的刻画.     

The Laplacian spectral radius for unicyclic graphs with given independence number

In this paper, we give a complete characterization of the extremal graphs with maximal Laplacian spectral radius among all unicyclic graphs with given order and given number of pendent vertices. Then we study the Laplacian spectral radius of unicyclic graphs with given independence number and characterize the extremal graphs completely.     

On the Laplacian spectral radius of weighted trees with a positive weight set

The spectrum of weighted graphs is often used to solve the problems in the design of networks and electronic circuits. We first give some perturbational results on the (signless) Laplacian spectral radius of weighted graphs when some weights of edges are modified; we then determine the weighted tree with the largest Laplacian spectral radius in the set of all weighted trees with a fixed number of pendant vertices and a positive weight set. Furthermore, we also derive the weighted trees with the largest Laplacian spectral radius in the set of all weighted trees with a fixed positive weight set and independence number, matching number or total independence number.     

The signless Laplacian spectral radius of graphs with given degree sequences

In this paper, we investigate the properties of the largest signless Laplacian spectral radius in the set of all simple connected graphs with a given degree sequence. These results are used to characterize the unicyclic graphs that have the largest signless Laplacian spectral radius for a given unicyclic graphic degree sequence. Moreover, all extremal unicyclic graphs having the largest signless Laplacian spectral radius are obtained in the sets of all unicyclic graphs of order n with a specified number of leaves or maximum degree or independence number or matching number.     

关于赋权树的谱半径的精确上界

The spectrum of weighted graphs are often used to solve the problems in the design of networks and electronic circuits. In this paper, we derive the sharp upper bound of spectral radius of all weighted trees on given order and edge independence number, and obtain all such trees that their spectral radius reach the upper bound.     

图的特征值交错方法的几个应用

本文利用特征值交错方法研究了图的谱半径下界等问题,得到了图谱半径的两个新的紧下界,以及图的Laplace谱与四边形个数的一个关系式.     

A Characterization of Graphs Where the Independence Number Equals the Radius

In a classical 1986 paper by Erdös, Saks and Saós every graph of radius r has an induced path of order at least 2r ? 1. This result implies that the independence number of such graphs is at least r. In this paper, we use a result of S. Fajtlowicz about radius-critical graphs to characterize graphs where the independence number is equal to the radius, for all possible values of the radius except 2, 3, and 4. We briefly discuss these remaining cases as well.     

The signless Laplacian spectral radius of bicyclic graphs with prescribed degree sequences

In this paper, we characterize all extremal connected bicyclic graphs with the largest signless Laplacian spectral radius in the set of all connected bicyclic graphs with prescribed degree sequences. Moreover, the signless Laplacian majorization theorem is proved to be true for connected bicyclic graphs. As corollaries, all extremal connected bicyclic graphs having the largest signless Laplacian spectral radius are obtained in the set of all connected bicyclic graphs of order n (resp. all connected bicyclic graphs with a specified number of pendant vertices, and all connected bicyclic graphs with given maximum degree).     

On the distance spectral radius of bipartite graphs

In this paper, we determine the unique graph with minimum distance spectral radius among all connected bipartite graphs of order $n$ with a given matching number. Moreover, we characterize the graphs with minimal distance spectral radius in the class of all connected bipartite graphs with a given vertex connectivity.     

Quotient of spectral radius, (signless) Laplacian spectral radius and clique number of graphs

In this paper, the upper and lower bounds for the quotient of spectral radius (Laplacian spectral radius, signless Laplacian spectral radius) and the clique number together with the corresponding extremal graphs in the class of connected graphs with n vertices and clique number ω(2 ≤ ω ≤ n) are determined. As a consequence of our results, two conjectures given in Aouchiche (2006) and Hansen (2010) are proved.