Bounds on graph eigenvalues II. Linear Algebra Appl., 427:183-189, 2007.V. Nikiforov.Bounds on graph eigenvalues Ⅱ. Linear Algebra and Its Applications . 2007V. Nikiforov: Bounds on graph eigenvalues II. Linear Algebra Appl. 427 (2007), 183-189....
Let G be a simple graph with n vertices.We denote by λ_i(G) the i-th largest eigenvalue of G.In this paper,several results are presented concerning bounds on the eigenvalues of G.In particular,it is shown that -1≤λ_2(G)≤(n-2)/2,and the left hand equality holds if and onl...
Let λ1(T) and λ2(T) be the largest and the second largest Laplacian eigenvalues of a tree T. We obtain the following sharp lower bound for λ1(T):λ1(T)⩾max(di+mi+1)+(di+mi+1)2−4(dimi+1)2:vi∈V,wheredi and mi denote the degree of vertex vi and the average of ...
based on a subgraph isomorphism and graph similarity search58,59,60, which has applications formulti-programmingon a quantum device61and may be of independent interest. In this case, however, it serves as a necessary step in our formulation and further enables...
A graph G of order n and size m is called an (n, m)-graph. In what follows we assume that the graph eigenvalues are labeled in a nonincreasing manner, i.e., λ1≥λ2≥⋯≥λ n . If G is connected, then...
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, ...
(G) the i-th largest eigenvalue of G.In this paper,several results are presented concerning bounds on the eigenvalues of G.In particular,it is shown that -1≤λ_2(G)≤(n-2)/2,and the left hand equality holds if and only if G is a complete graph with at least two vertices;the ...
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...
We first apply non-negative matrix theory to the matrix K = D + A, where D and A are the degree-diagonal and adjacency matrices of a graph G, respectively, to establish a relation on the largest Laplacian eigenvalue λ1 (G) of G and the spectral radius p(K) of K. And then by ...
We provide upper bounds on the perturbation of invariant subspaces of normal matrices measured using a metric on the space of vector subspaces of $\mathbb{C}^{n}$ in terms of the spectrum of both unperturbed and perturbed matrices as well as the spectrum