let $n$ be any positive integer, the friendship graph $f_n$ consists of $n$ edge-disjoint triangles that all of them meeting in one vertex. a graph $g$ is called cospectral with a graph $h$ if their adjacency matrices have the same eigenvalues. recently in href{http://arxiv.org/pdf/1310.6529v1.pdf}{http://arxiv.org/pdf/1310.6529v1.pdf} it is proved that if $g$ is any graph cospectral with $f_n$...

let $g$ be a simple graph with vertex set $v(g) = {v_1, v_2,ldots, v_n}$ and $d_i$ the degree of its vertex $v_i$, $i = 1, 2,cdots, n$. inspired by the randi'c matrix and the general randi'cindex of a graph, we introduce the concept of general randi'cmatrix $textbf{r}_alpha$ of $g$, which is defined by$(textbf{r}_alpha)_{i,j}=(d_id_j)^alpha$ if $v_i$ and $v_j$ areadjacent, and zero otherwise. s...

in this paper, we present some inequalities for the co-pi index involving the some topological indices, the number of vertices and edges, and the maximum degree. after that, we give a result for trees. in addition, we give some inequalities for the largest eigenvalue of the co-pi matrix of g.

Geometric modeling is the branch of applied mathematics devoted to methods and algorithms for mathematical description of shapes. Two-dimensional models are of crucial interest in design, technical drawing and computer typography, while three-dimensional models are central to computer-aided-geometric-design (CAGD) and computer-aided-manufacturing (CAM), and widely used in many applied technical...

The geometric optics stability method is extended to a general class of linear advective PDE’s with pseudodifferential bounded perturbation. We give a new short proof of Vishik’s formula for the essential spectral radius. We show that every point in the dynamical spectrum of the corresponding bicharacteristicamplitude system contributes a point into the essential spectrum of the PDE. Generic sp...

The famous Gelfand formula ρ(A) = lim supn→∞ ‖A ‖ for the spectral radius of a matrix is of great importance in various mathematical constructions. Unfortunately, the range of applicability of this formula is substantially restricted by a lack of estimates for the rate of convergence of the quantities ‖A‖ to ρ(A). In the paper this deficiency is made up to some extent. By using the Bochi inequa...

We prove new inequalities for the spectral radius, essential operator norm, measure of noncompactness and numerical radius Hadamard weighted geometric means positive kernel operators on Banach function sequence spaces. Some extend refine known that have been established by several authors relatively recently. Several appear to be even in finite dimensional case.

This paper proposes lower bounds on a quantity called L-norm joint spectral radius, or in short, p-radius, of a finite set of matrices. Despite its wide range of applications to, for example, stability analysis of switched linear systems and the equilibrium analysis of switched linear economical models, algorithms for computing the p-radius are only available in a very limited number of particu...

The joint spectral radius of a set of matrices is a measure of the maximal asymptotic growth rate that can be obtained by forming long products of matrices taken from the set. This quantity appears in a number of application contexts but is notoriously difficult to compute and to approximate. We introduce in this paper an approximation ρ̂ that is based on ellipsoid norms, that can be computed by...