We give an upper bound for the largest eigenvalue of a nonregular graph with n vertices and the largest vertex degree ∆.

This paper derives a posteriori error estimates for conforming numerical approximations of the Laplace eigenvalue problem with a homogeneous Dirichlet boundary condition. In particular, upper and lower bounds for an arbitrary simple eigenvalue are given. These bounds are guaranteed, fully computable, and converge with optimal speed to the given exact eigenvalue. They are valid without restricti...

Abstract. We consider ensembles of random matrices, known as biorthogonal ensembles, whose eigenvalue probability density function can be written as a product of two determinants. These systems are closely related to multiple orthogonal functions. It is known that the eigenvalue correlation functions of such ensembles can be written as a determinant of a kernel function. We show that the kernel...

We study the Steiner k-eccentricity on trees, which generalizes previous one in paper [On average 3-eccentricity of arXiv:2005.10319]. achieve much stronger properties for k-ecc tree than that paper. Based this, a linear time algorithm is devised to calculate vertex tree. On other hand, lower and upper bounds index order n are established based novel technique quite different also easier follow...

The aim of this article is to analyse cone density, spacing and arrangement using an adaptive optics flood illumination retina camera (rtx1™) on a healthy population. Cone density, cone spacing and packing arrangements were measured on the right retinas of 109 subjects at 2°, 3°, 4°, 5° and 6° of eccentricity along 4 meridians. The effects of eccentricity, meridian, axial length, spherical equi...

The eccentric connectivity index based on degree and eccentricity of the vertices of a graph is a widely used graph invariant in mathematics. In this paper we present the explicit generalized expressions for the eccentric connectivity index and polynomial of the thorn graphs, and then consider some particular cases.

We investigate the noise sensitivity of top eigenvector a sparse random symmetric matrix. Let v be an N×N matrix with average d non-zero centered entries per row. resample k randomly chosen and obtain another realization v[k]. Building on recent results matrices analysis previously developed for Wigner matrices, we prove that, if d?N2?9, high probability, when k?N5?3, vectors v[k] are almost co...

In this study, the effective parameters on the inelastic response of asymmetric buildings is evaluated for an ensemble of real Iranian earthquake records by considering soil-structure interaction. Then, the design eccentricity obtained from the inelastic dynamic soil-structure analysis is compared with the design eccentricity of seisimic codes of Iran, ATC-3, New Zeland, Canada, Mexico, Austral...

For a connected graph G, we derive tight inequalities relating the smallest signless Laplacian eigenvalue to the largest normalised Laplacian eigenvalue. We investigate how vectors yielding small values of the Rayleigh quotient for the signless Laplacian matrix can be used to identify bipartite subgraphs. Our results are applied to some graphs with degree sequences approximately following a pow...