V. Nikiforov, Bounds on graph eigenvalues II, Linear Algebra Appl., 427 (2007) 183-189.V. Nikiforov, Bounds on graph eigenvalues II, available at http://arxiv.org/abs/math.CO/0612461V. Nikiforov, Bounds on graph eigenvalues II, to appear in Linear Algebra Appl....
The largest eigenvalues of A(G) and Q(G) are called the index and the Q-index (denoted by q(G)) of G, respectively. For a connected graph G, by the Perron–Frobenius theory of non-negative matrices, q(G) has multiplicity one and there exists a unique positive unit eigenvector ...
an upper bound on the distance (in terms of d_{\mathrm{{sp}}}) between the invariant subspaces \operatorname{span}(\mathbf{u}_{J}) and \operatorname{span}(\widetilde{\mathbf{u}}_{\widetilde{J}}) in terms of the distance between the matrices M and M̃ and their eigenvalues. For...
Bounds of the Laplacian spectral radius of a graph 来自 Semantic Scholar 喜欢 0 阅读量: 15 作者: C Wang 摘要: An inequality on eigenvalues is presented.We apply it to estimate the eigenvalues of the Laplacian matrix L(G)of a graph G=(V,E).关键词:...
for an orthonormal basis\(\{\left\vert {\psi }_{j}\right\rangle \}\), wherepjare non-negative eigenvalues summing to 1. In this work, as in ref.39,40, we make use of the concept of a density matrix to describe a complex network (i.e. a graph with many edges and vertices, ...
for an orthonormal basis\(\{\left\vert {\psi }_{j}\right\rangle \}\), wherepjare non-negative eigenvalues summing to 1. In this work, as in ref.39,40, we make use of the concept of a density matrix to describe a complex network (i.e. a graph with many edges and vertices, ...
We refer to x and y as N -particle configurations (briefly, configurations) on Z and use the same notation d(x, y) for the graph distance on ZN (as before, d(x, x) = 0). Apart from the distance d(· , ·) on ZN , it will be convenient to use the max-distance ρ and ...
Adjacency matrixEigenvaluesSpectral radiusWe obtain bounds for the largest and least eigenvalues of the adjacency matrix of a simple undirected graph. We find upper bound for the second largest eigenvalue of the adjacency matrix. We prove that the bounds obtained here improve on the existing bounds...
In this paper we give three upper bounds for the largest of minimum degree Laplacian eigenvalues of a graph and also obtain a lower bound for the same. Key Words: Minimum degree matrix, minimum degree Laplacian eigenvalues. AMS(20 10): 05C50Adiga, ChandrashekarSwamy, C. S. Shivakumar...
Jiong Sheng Li,Yong Liang Pan.Upper Bounds for the Laplacian Graph Eigenvalues[J]. Acta Mathematica Sinica, English Series .2004(5)D.M. Zhu, On upper bounds for Laplacian graph eigenvalues, Linear Algebra Appl. 432 (2010) 2764-2772