共查询到20条相似文献,搜索用时 15 毫秒
1.
Peng Xiao 《Linear and Multilinear Algebra》2019,67(7):1392-1403
In this paper, we introduce the operations of grafting an edge and subdividing an edge on hypergraphs, and consider how spectral radius of a hypergraph behaves by grafting an edge or subdividing an edge. As an application, we determine the unique hypergraphs with the maximum spectral radius among all the uniform supertrees and all the connected uniform unicyclic hypergraphs with given number of pendant edges, respectively. Moreover, we determine the unique uniform supertree which attains the maximum spectral radius among all the uniform supertrees with given number of pendant vertices. 相似文献
2.
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
3.
4.
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
5.
In this paper, the effects on the signless Laplacian spectral radius of a graph are studied when some operations, such as
edge moving, edge subdividing, are applied to the graph. Moreover, the largest signless Laplacian spectral radius among the
all unicyclic graphs with n vertices and k pendant vertices is identified. Furthermore, we determine the graphs with the largest
Laplacian spectral radii among the all unicyclic graphs and bicyclic graphs with n vertices and k pendant vertices, respectively. 相似文献
6.
In this paper, we give some results on Laplacian spectral radius of graphs with cut vertices, and as their applications, we also determine the unique graph with the largest Laplacian spectral radius among all unicyclic graphs with n vertices and diameter d, 3?d?n−3. 相似文献
7.
A unicyclic graph is a graph whose number of edges is equal to the number of vertices. Guo Shu-Guang [S.G. Guo, The largest Laplacian spectral radius of unicyclic graph, Appl. Math. J. Chinese Univ. Ser. A. 16 (2) (2001) 131–135] determined the first four largest Laplacian spectral radii together with the corresponding graphs among all unicyclic graphs on n vertices. In this paper, we extend this ordering by determining the fifth to the ninth largest Laplacian spectral radii together with the corresponding graphs among all unicyclic graphs on n vertices. 相似文献
8.
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
9.
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
10.
The Laplacian spectral radii of unicyclic and bicyclic graphs with n vertices and k pendant vertices
JiMing Guo 《中国科学 数学(英文版)》2010,53(8):2135-2142
In this paper, we determine graphs with the largest Laplacian spectral radius among the unicyclic and the bicyclic graphs on n vertices with k pendant vertices, respectively. 相似文献
11.
Let 𝒰(n,?d) be the class of unicyclic graphs on n vertices with diameter d. This article presents an edge-grafting theorem on Laplacian spectra of graphs. By applying this theorem, we determine the unique graph with the maximum Laplacian spectral radius in 𝒰(n,?d). This extremal graph is different from that for the corresponding problem on the adjacency spectral radius as done by Liu et al. [Q. Liu, M. Lu, and F. Tian, On the spectral radius of unicyclic graphs with fixed diameter, Linear Algebra Appl. 420 (2007), 449–457]. 相似文献
12.
设U*为一个未定向的n个顶点上的单圈混合图,它是由一个三角形在其某个顶点上附加n-3个悬挂边而获得.在文[Largest eigenvalue of a unicyclic mixed graph,Applied Mathematics A Journal of Chinese Universities(Ser.B),2004,19(2):140-148]中,作者证明了:在相差符号同构意下,在所有n个顶点上的单圈混合图中,U*是唯一的达到最大Laplace谱半径的混合图.本文应用非负矩阵的Perron向量,给出上述结论的一个简单的证明. 相似文献
13.
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. 相似文献
14.
设U*为一个未定向的n个顶点上的单圈混合图,它是由一个三角形在其某个顶点上附加”一3个悬挂边而获得.在文[Largest eigenvalue of aunicyclic mixed graph,Applied Mathematics A Journal of Chinese Universities (Ser.B),2004,19(2):140-J48]中,作者证明了:在相差符号同构意下,在所有n个顶点上的单圈混合图中,U*是唯一的达到最大Laplace谱半径的混合图.本文应用非负矩阵的Perron向量,给出上述结论的一个简单的证明. 相似文献
15.
16.
A supertree is a connected and acyclic hypergraph. For a hypergraph H, the maximal modulus of the eigenvalues of its adjacency tensor is called the spectral radius of H. By applying the operation of moving edges on hypergraphs and the weighted incidence matrix method, we determine the ninth and the tenth k-uniform supertrees with the largest spectral radii among all k-uniform supertrees on n vertices, which extends the known result. 相似文献
17.
The normalized Laplacian eigenvalues of a network play an important role in its structural and dynamical aspects associated with the network. In this paper, we consider how the normalized Laplacian spectral radius of a non-bipartite graph behaves by several graph operations. As an example of the application, the smallest normalized Laplacian spectral radius of non-bipartite unicyclic graphs with fixed order is determined. 相似文献
18.
A supertree is a connected and acyclic hypergraph. We investigate the supertrees with the extremal spectral radii among several kinds of r-uniform supertrees. First, by using the matching polynomials of supertrees, a new and useful grafting operation is proposed for comparing the spectral radii of supertrees, and its applications are shown to obtain the supertrees with the extremal spectral radii among some kinds of r-uniform supertrees. Second, the supertree with the third smallest spectral radius among the r-uniform supertrees is deduced. Third, among the r-uniform supertrees with a given maximum degree, the supertree with the smallest spectral radius is derived. At last, among the r-uniform starlike supertrees, the supertrees with the smallest and the largest spectral radii are characterized. 相似文献
19.
Let U(n,d) be the set of unicyclic graphs on n vertices with diameter d. In this article, we determine the unique graph with minimal least eigenvalue among all graphs in U(n,d). It is found that the extremal graph is different from that for the corresponding problem on maximal eigenvalue as done by Liu et al. [H.Q. Liu, M. Lu, F. Tian, On the spectral radius of unicyclic graphs with fixed diameter, Linear Algebra Appl. 420 (2007) 449-457]. 相似文献
20.
Xiaoling Zhang 《Linear algebra and its applications》2012,437(7):1930-1941
For a connected graph, the distance spectral radius is the largest eigenvalue of its distance matrix. In this paper, we determine the unique graph with minimum distance spectral radius among all connected graphs of order n with a given diameter. Moreover, we determine the unique graph with maximum distance spectral radius among the catacondensed hexagonal systems with h hexagons. 相似文献