It is shown that if a d-regular graph contains s vertices so that the distance between any pair is at least 4k, then its adjacency matrix has at least s eigenvalues which are at least 2 √ d − 1 cos( π 2k ). A similar result has been proved by Friedman using more sophisticated tools.

In this paper we will prove that μ(G) + μ(G) ≤ 1 + √ 3 2 n − 1 where μ(G), μ(G) are the greatest eigenvalues of the adjacency matrices of the graph G and its complement and n denotes the number of vertices of G.

Let G be a simple graph of order n, let λ1(G), λ2(G), . . . , λn(G) be the eigenvalues of the adjacency matrix of G. The Esrada index of G is defined as EE(G) = ∑n i=1 e i. In this paper we determine the unique graph with maximum Estrada index among bicyclic graphs with fixed order.

Let G be a connected graph of order n. The diameter of a graph is the maximum distance between any two vertices of G. In this paper, we will give some bounds on the diameter of G in terms of eigenvalues of adjacency matrix and Laplacian matrix, respectively.

The spectral radius (or the signless Laplacian radius) of a general hypergraph is maximum modulus eigenvalues its adjacency Laplacian) tensor. In this paper, we firstly obtain lower bound hypergraphs in terms clique number. Moreover, present relation between homogeneous polynomial and number hypergraphs. As an application, finally upper

Abstract Adjacency matrix A(G)=[aij] yields the graph energy, which is equal to addition of absolute values eigenvalues G. This research investigates energy class in terms another after removing a vertex. After deleting vertex, relationship between complete E[ k n ] and splitting E(S’ [ ]) discovered.

We analyze protein-protein interaction networks for six different species under the framework of random matrix theory. Nearest neighbor spacing distribution of the eigenvalues of adjacency matrices of the largest connected part of these networks emulate universal Gaussian orthogonal statistics of random matrix theory. We demonstrate that spectral rigidity, which quantifies long range correlatio...

In this paper, we focus on differential privacy preserving spectral graph analysis. Spectral graph analysis deals with the analysis of the spectra (eigenvalues and eigenvector components) of the graph’s adjacency matrix or its variants. We develop two approaches to computing the ε-differential eigen decomposition of the graph’s adjacency matrix. The first approach, denoted as LNPP, is based on ...

We initiate the study of pretty good quantum fractional revival in graphs, a generalization state transfer graphs. give complete characterization graph terms eigenvalues and eigenvectors adjacency matrix graph. This follows from lemma due to Kronecker on Diophantine approximation, is similar spectral Using this, we characterizations when can occur paths cycles.