共查询到10条相似文献,搜索用时 78 毫秒
1.
Luhua Wang 《Linear and Multilinear Algebra》2013,61(12):2396-2405
A clover graph is obtained from a 3-rose graph by attaching a path to the vertex of degree six, where a 3-rose graph consists of three cycles with precisely one common vertex. In this paper, it is proved that all clover graphs are determined by their Laplacian spectra. 相似文献
2.
Xiaoling Ma 《Linear and Multilinear Algebra》2016,64(12):2474-2485
A rose graph with p petals (or p-rose graph) is a graph obtained by taking p cycles with just a vertex in common. In this paper, we prove that all 4-rose graphs are determined by their signless Laplacian spectra. 相似文献
3.
A graph is called Laplacian integral if all its Laplacian eigenvalues are integers. In this paper, we give an edge subdividing theorem for Laplacian eigenvalues of a graph (Theorem 2.1) and characterize a class of k-cyclic graphs whose algebraic connectivity is less than one. Using these results, we determine all the Laplacian integral tricyclic graphs. Furthermore, we show that all the Laplacian integral tricyclic graphs are determined by their Laplacian spectra. 相似文献
4.
Let M be an associated matrix of a graph G (the adjacency, Laplacian and signless Laplacian matrix). Two graphs are said to be cospectral with respect to M if they have the same M spectrum. A graph is said to be determined by M spectrum if there is no other non-isomorphic graph with the same spectrum with respect to M. It is shown that T-shape trees are determined by their Laplacian spectra. Moreover among them those are determined by their adjacency spectra are characterized. In this paper, we identify graphs which are cospectral to a given T-shape tree with respect to the signless Laplacian matrix. Subsequently, T-shape trees which are determined by their signless Laplacian spectra are identified. 相似文献
5.
The second largest Laplacian eigenvalue of a graph is the second largest eigenvalue of the associated Laplacian matrix. In this paper, we study extremal graphs for the extremal values of the second largest Laplacian eigenvalue and the Laplacian separator of a connected graph, respectively. All simple connected graphs with second largest Laplacian eigenvalue at most 3 are characterized. It is also shown that graphs with second largest Laplacian eigenvalue at most 3 are determined by their Laplacian spectrum. Moreover, the graphs with maximum and the second maximum Laplacian separators among all connected graphs are determined. 相似文献
6.
A Π-shape tree is a tree with exactly two vertices having the maximum degree three. In this paper, we classify the Π-shape trees into two types, and complete the spectral characterization for one type. Exactly, we prove that all graphs of this type are determined by their Laplacian spectra with some exceptions. Moreover, we give some L-cospectral mates of some graphs for another type. 相似文献
7.
G.R. Omidi 《Linear algebra and its applications》2008,428(7):1696-1705
A graph is said to be determined by the adjacency and Laplacian spectrum (or to be a DS graph, for short) if there is no other non-isomorphic graph with the same adjacency and Laplacian spectrum, respectively. It is known that connected graphs of index less than 2 are determined by their adjacency spectrum. In this paper, we focus on the problem of characterization of DS graphs of index less than 2. First, we give various infinite families of cospectral graphs with respect to the adjacency matrix. Subsequently, the results will be used to characterize all DS graphs (with respect to the adjacency matrix) of index less than 2 with no path as a component. Moreover, we show that most of these graphs are DS with respect to the Laplacian matrix. 相似文献
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9.
设 H(K_{1,5},P_n,C_l)是由路 P_n的两个悬挂点分别粘上星图K_{1,5}的悬挂点和圈 C_l的点所得的单圈图. 若两个二部图是关于Laplacian 矩阵同谱的, 则它们的线图是邻接同谱的, 两个邻接同谱图含有相同数目的同长闭回路. 如果任何一个与图G关于Laplacian 同谱图都与图G 同构, 那么称图G可由其Laplacian 谱确定. 利用图与线图之间的关系证明了H(K_{1,5},P_n,C_4)、H(K_{1,5},P_n,C_6) 由它们的Laplacian谱确定. 相似文献
10.
In Wang and Xu (2006) [15] and [16] the authors introduced a family of graphs Hn and gave some methods for finding graphs among this family that are determined by their generalized spectra. This paper is a continuation of our previous work. We further show that almost all graphs in Hn are determined by their generalized spectra. This gives some evidences for the conjecture that almost all graphs are determined by their generalized spectra. 相似文献