Two shorter proofs in spectral graph theory

Two Shorter Proofs in Spectral Graph Theory

Let G be a simple graph with V (E) as its vertex (respectively, edge) set. The spectrum of G is the spectrum of its adjacency matrix. For all other definitions (or notation not given here), especially those related to graph spectra, see [1]. The purpose of this note is to provide shorter proofs of two inequalities already known in spectral graph theory. The first bounds vertex eccentricities of...

Spectral graph theory

With every graph (or digraph) one can associate several different matrices. We have already seen the vertex-edge incidence matrix, the Laplacian and the adjacency matrix of a graph. Here we shall concentrate mainly on the adjacency matrix of (undirected) graphs, and also discuss briefly the Laplacian. We shall show that spectral properies (the eigenvalues and eigenvectors) of these matrices pro...

Spectral graph theory

Spectral graph theory

Spectral graph theory is a fast developing field in modern discrete mathematics with important applications in computer science, chemistry and operational research. By merging combinatorial techniques with algebraic and analytical methods it creates new approaches to hard discrete problems and gives new insights in classical Linear Algebra. The proposed minisymposium will bring together leading...

Spectral graph theory

Let us first review some basic random graph models. The most popular is perhaps the Erdös-Rényi model, denoted by G(n, p) for some n ∈ N and p ∈ [0, 1]. In this model, there is a set of vertices V (with n = |V |), and the edge set over V is determined randomly by ( n 2 ) biased coin tosses. Initially, there are no edges: E := ∅. Then, for each pair of vertices u, v ∈ V , independently flip a co...