Let Hn（p,q） be a tree obtained from two stars K1,p and K1,q by identifying the center of K1,p with one end of a path Pn and the center of K1,q with the other end of Pn.We call Hn（p,p-1） a double quasi-star tree.In...Let Hn（p,q） be a tree obtained from two stars K1,p and K1,q by identifying the center of K1,p with one end of a path Pn and the center of K1,q with the other end of Pn.We call Hn（p,p-1） a double quasi-star tree.In this paper,we show that a double quasi-star tree is determined by its Laplacian spectrum.展开更多
Let T be a tree with matching number μ(T). In this paper we obtain the following result: If T has no perfect matchings, thenμ(T) is a lower bound for the number of nonzero Laplacian eigenvalues of T which are smalle...Let T be a tree with matching number μ(T). In this paper we obtain the following result: If T has no perfect matchings, thenμ(T) is a lower bound for the number of nonzero Laplacian eigenvalues of T which are smaller than 2.展开更多
The spectrum of a graph is the set of all eigenvalues of the Laplacian matrix of the graph. There is a closed relationship between the Laplacian spectrum of graphs and some properties of graphs such as connectivity. I...The spectrum of a graph is the set of all eigenvalues of the Laplacian matrix of the graph. There is a closed relationship between the Laplacian spectrum of graphs and some properties of graphs such as connectivity. In the recent years Laplacian spectrum of graphs has been widely applied in many fields. The application of Laplacian spectrum of graphs to circuit partitioning problems is reviewed in this paper. A new criterion of circuit partitioning is proposed and the bounds of the partition ratio for weighted graphs are also presented. Moreover, the deficiency of graph-partitioning algorithms by Laplacian eigenvectors is addressed and an algorithm by means of the minimal spanning tree of a graph is proposed. By virtue of taking the graph structure into consideration this algorithm can fulfill general requirements of circuit partitioning.展开更多
This paper is conceraing with the estimate of the first eigenvalue of hyper surface embedded in a compact manifolds with positive ined curvature.It leads to an upper bound of area of compact Riemannian surface embedde...This paper is conceraing with the estimate of the first eigenvalue of hyper surface embedded in a compact manifolds with positive ined curvature.It leads to an upper bound of area of compact Riemannian surface embedded in S3. Secondly,spectral isomorphic problem is discussed.展开更多
Given graphs Gand G, we define a graph operation on Gand G,namely the SSG-vertex join of Gand G, denoted by G★ G. Let S(G) be the subdivision graph of G. The SSG-vertex join G★Gis the graph obtained from S(G) and S(...Given graphs Gand G, we define a graph operation on Gand G,namely the SSG-vertex join of Gand G, denoted by G★ G. Let S(G) be the subdivision graph of G. The SSG-vertex join G★Gis the graph obtained from S(G) and S(G) by joining each vertex of Gwith each vertex of G. In this paper, when G(i = 1, 2) is a regular graph, we determine the normalized Laplacian spectrum of G★ G. As applications, we construct many pairs of normalized Laplacian cospectral graphs, the normalized Laplacian energy, and the degree Kirchhoff index of G★G.展开更多
For a simple graph G,let matrix Q(G)=D(G) + A(G) be it's signless Laplacian matrix and Q G (λ)=det(λI Q) it's signless Laplacian characteristic polynomial,where D(G) denotes the diagonal matrix of vertex deg...For a simple graph G,let matrix Q(G)=D(G) + A(G) be it's signless Laplacian matrix and Q G (λ)=det(λI Q) it's signless Laplacian characteristic polynomial,where D(G) denotes the diagonal matrix of vertex degrees of G,A(G) denotes its adjacency matrix of G.If all eigenvalues of Q G (λ) are integral,then the graph G is called Q-integral.In this paper,we obtain that the signless Laplacian characteristic polynomials of the complete multi-partite graphs G=K(n_1,n_2,···,n_t).We prove that the complete t-partite graphs K(n,n,···,n)t are Q-integral and give a necessary and sufficient condition for the complete multipartite graphs K(m,···,m)s(n,···,n)t to be Q-integral.We also obtain that the signless Laplacian characteristic polynomials of the complete multipartite graphs K(m,···,m,)s1(n,···,n,)s2(l,···,l)s3.展开更多
基金Project supported by the Natural Science Foundation of Gausu Province (Grant Nos.3Z5051-A25-037, 0809RJZA017)the National Natural Science Foundation of China (Grant No.50877034)the Foundation of Lanzhou University of Technology(Grant No.0914ZX136)
文摘Let Hn（p,q） be a tree obtained from two stars K1,p and K1,q by identifying the center of K1,p with one end of a path Pn and the center of K1,q with the other end of Pn.We call Hn（p,p-1） a double quasi-star tree.In this paper,we show that a double quasi-star tree is determined by its Laplacian spectrum.
基金This research is supported by Anhui provincial Natural Science Foundation, Natural Science Foundation of Department of Education of Anhui Province of China (2004kj027)the Project of Research for Young Teachers of Universities of Anhui Province of China (2003jql01)and the Project of Anhui University for Talents Group Construction.
文摘Let T be a tree with matching number μ(T). In this paper we obtain the following result: If T has no perfect matchings, thenμ(T) is a lower bound for the number of nonzero Laplacian eigenvalues of T which are smaller than 2.
基金This work was supported in part by the National Natural Science Foundation of China(Grant Nos.60025101 and 90207001)by the National Basic Research Priorities Program(Contract No.G1999032903).
文摘The spectrum of a graph is the set of all eigenvalues of the Laplacian matrix of the graph. There is a closed relationship between the Laplacian spectrum of graphs and some properties of graphs such as connectivity. In the recent years Laplacian spectrum of graphs has been widely applied in many fields. The application of Laplacian spectrum of graphs to circuit partitioning problems is reviewed in this paper. A new criterion of circuit partitioning is proposed and the bounds of the partition ratio for weighted graphs are also presented. Moreover, the deficiency of graph-partitioning algorithms by Laplacian eigenvectors is addressed and an algorithm by means of the minimal spanning tree of a graph is proposed. By virtue of taking the graph structure into consideration this algorithm can fulfill general requirements of circuit partitioning.
文摘This paper is conceraing with the estimate of the first eigenvalue of hyper surface embedded in a compact manifolds with positive ined curvature.It leads to an upper bound of area of compact Riemannian surface embedded in S3. Secondly,spectral isomorphic problem is discussed.
文摘Given graphs Gand G, we define a graph operation on Gand G,namely the SSG-vertex join of Gand G, denoted by G★ G. Let S(G) be the subdivision graph of G. The SSG-vertex join G★Gis the graph obtained from S(G) and S(G) by joining each vertex of Gwith each vertex of G. In this paper, when G(i = 1, 2) is a regular graph, we determine the normalized Laplacian spectrum of G★ G. As applications, we construct many pairs of normalized Laplacian cospectral graphs, the normalized Laplacian energy, and the degree Kirchhoff index of G★G.
基金Supported by the NSFC(60863006)Supported by the NCET(-06-0912)Supported by the Science-Technology Foundation for Middle-aged and Yong Scientist of Qinghai University(2011-QGY-8)
文摘For a simple graph G,let matrix Q(G)=D(G) + A(G) be it's signless Laplacian matrix and Q G (λ)=det(λI Q) it's signless Laplacian characteristic polynomial,where D(G) denotes the diagonal matrix of vertex degrees of G,A(G) denotes its adjacency matrix of G.If all eigenvalues of Q G (λ) are integral,then the graph G is called Q-integral.In this paper,we obtain that the signless Laplacian characteristic polynomials of the complete multi-partite graphs G=K(n_1,n_2,···,n_t).We prove that the complete t-partite graphs K(n,n,···,n)t are Q-integral and give a necessary and sufficient condition for the complete multipartite graphs K(m,···,m)s(n,···,n)t to be Q-integral.We also obtain that the signless Laplacian characteristic polynomials of the complete multipartite graphs K(m,···,m,)s1(n,···,n,)s2(l,···,l)s3.
