共查询到20条相似文献,搜索用时 31 毫秒
1.
Shang-wang Tan 《Discrete Mathematics》2010,310(5):1026-1212
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. 相似文献
2.
Xiao-Dong Zhang 《Discrete Mathematics》2008,308(15):3143-3150
In this paper, we characterize all extremal trees with the largest Laplacian spectral radius in the set of all trees with a given degree sequence. Consequently, we also obtain all extremal trees with the largest Laplacian spectral radius in the sets of all trees of order n with the largest degree, the leaves number and the matching number, respectively. 相似文献
3.
Xiao-Dong Zhang 《Discrete Applied Mathematics》2009,157(13):2928-2937
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. 相似文献
4.
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). 相似文献
5.
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. 相似文献
6.
关于谱半径达到第二大的赋权树 总被引:1,自引:0,他引:1
赋权图的谱的研究已经被用来解决很多实际问题,网络设计以及电路设计实际上都依赖于赋权图.本文主要研究的是赋权树的谱半径,从而得到赋权树谱半径达到次大的是双星图Sn-3,1ω*. 相似文献
7.
We consider the set of unicyclic graphs with prescribed degree sequence. In this set we determine the (unique) graph with the largest spectral radius (or index) with respect to the adjacency matrix. In addition, we give a conjecture about the (unique) graph with the largest index in the set of connected graphs with prescribed degree sequence. 相似文献
8.
The Laplacian spectral radius of a graph is the largest eigenvalue of the associated Laplacian matrix. In this paper, we provide structural and behavioral details of graphs with maximum Laplacian spectral radius among all bipartite connected graphs of given order and size. Using these results, we provide a unified approach to determine the graphs with maximum Laplacian spectral radii among all trees, and all bipartite unicyclic, bicyclic, tricyclic and quasi-tree graphs, respectively. 相似文献
9.
图的邻接矩阵的最大特征值称为图的谱半径.对于n≥8,1≤k≤n+23,本文确定了n个顶点和至少有惫个顶点度不少于3的树中具有谱半径最大的树. 相似文献
10.
Let T(n,i) be the set of all trees with order n and matching number i.We determine the third to sixth trees in T(2i + 1,i) and the third to fifth trees in T(n,i) for n ≥ 2i + 2 with the largest Laplacian spectral radius. 相似文献
11.
A semiregular tree is a tree where all non-pendant vertices have the same degree. Among all semiregular trees with fixed order and degree, a graph with minimal (adjacency/Laplacian) spectral radius is a caterpillar. Counter examples show that the result cannot be generalized to the class of trees with a given (non-constant) degree sequence. 相似文献
12.
Let G be a simple connected graph with pendant vertex set ?V and nonpendant vertex set V_0. The signless Laplacian matrix of G is denoted by Q(G). The signless Dirichlet eigenvalue is a real number λ such that there exists a function f ≠ 0 on V(G) such that Q(G)f(u) = λf(u) for u ∈ V_0 and f(u) = 0 for u ∈ ?V. The signless Dirichlet spectral radiusλ(G) is the largest signless Dirichlet eigenvalue. In this paper, the unicyclic graphs with the largest signless Dirichlet spectral radius among all unicyclic graphs with a given degree sequence are characterized. 相似文献
13.
Let 𝒯(n,?r;?W n?1) be the set of all n-vertex weighted trees with r vertices of degree 2 and fixed positive weight set W n?1, 𝒫(n,?γ;?W n?1) the set of all n-vertex weighted trees with q pendants and fixed positive weight set W n?1, where W n?1?=?{w 1,?w 2,?…?,?w n?1} with w 1???w 2???···???w n?1?>?0. In this article, we first identify the unique weighted tree in 𝒯(n,?r;?W n?1) with the largest adjacency spectral radius. Then we characterize the unique weighted trees with the largest adjacency spectral radius in 𝒫(n,?γ;?W n?1). 相似文献
14.
This paper studies the problem of estimating the spectral radius of trees with the given number of vertices and maximum degree. We obtain the new upper bounds on the spectral radius of the trees, and the results are the best upper bounds expressed by the number of vertices and maximum degree, at present. 相似文献
15.
Ai-mei Yu 《应用数学学报(英文版)》2014,30(4):1107-1112
Let T be a tree with n vertices and let A(T) be the adjacency matrix of T. Spectral radius of T is the largest eigenvalue of A(T). Wu et al. [Wu, B.F., Yuan, X.Y, and Xiao, E.L. On the spectral radii of trees, Journal of East China Normal University (Natural Science), 3:22-28 (2004)] determined the first seven trees of order n with the smallest spectral radius. In this paper, we extend this ordering by determining the trees with the eighth to the tenth smallest spectral radius among all trees with n vertices. 相似文献
16.
17.
Hongying Lin 《Linear and Multilinear Algebra》2019,67(2):370-390
The unique graphs with maximum distance spectral radius among trees with given number of vertices of maximum degree and among homeomorphically irreducible trees, respectively, are determined. 相似文献
18.
Yingluan Liu 《Linear algebra and its applications》2010,433(5):1015-1023
Restricted to the bicyclic graphs with prescribed degree sequences, we determine the (unique) graph with the largest spectral radius with respect to the adjacency matrix. 相似文献
19.