A divisible design graph is a graph whose adjacency matrix is the incidence matrix of a divisible design. These graphs are a natural generalization of (v, k, ⋋)-graphs. In this paper we develop some theory, find many parameter conditions and give several constructions

We construct graphs that are cospectral but nonisomorphic with Kneser graphs K(n, k), when n =3k - 1, k> 2 and for infinitely many other pairs (n, k). We also prove that for 3 ≤ k ≤ n - 3 the Modulo-2 Kneser graph K2(n, k) is not determined by the spectrum

This contribution presents an overview of sensitivity analysis of simulation models, including the estimation of gradients. It covers classic designs and their corresponding (meta)models; namely, resolution-III designs including fractional-factorial two-level designs for first-order polynomial...

Managers wish to verify that a particular engineering design meets their requirements. This design's future environment will differ from the environment assumed during the design. Therefore it is crucial to determine which variations in the environment may make this design unacceptable. The...

Sequential bifurcation (or SB) is an efficient and effective factor-screening method; i.e., SB quickly identifies the important factors (inputs) in experiments with simulation models that have very many factors — provided the SB assumptions are valid. The specific SB assumptions are: (i) a...

This chapter surveys two methods for the optimization of real-world systems that are modelled through simulation. These methods use either linear regression metamodels, or Kriging (Gaussian processes). The metamodel type guides the design of the experiment; this design fixes the input...

This tutorial reviews the design and analysis of simulation experiments. These experiments may have various goals: validation, prediction, sensitivity analysis, optimization (possibly robust), and risk or uncertainty analysis. These goals may be realized through metamodels. Two types of...

In this chapter we present Kriging also known as a Gaussian process (GP) model which is a mathematical interpolation method. To select the input combinations to be simulated, we use Latin hypercube sampling (LHS); we allow uniform and non-uniform distributions of the simulation inputs. Besides...

Let k be a natural number and let G be a graph with at least k vertices. A.E. Brouwer conjectured that the sum of the k largest Laplacian eigenvalues of G is at most e(G) (k choose 2), where e(G) is the number of edges of G. We prove this conjecture for k = 2. We also show that if G is a tree,...

We study graphs with spectral radius at most $\frac{3}{2}\sqrt{2}$ and refine results by Woo and Neumaier [On graphs whose spectral radius is bounded by $\frac{3}{2}\sqrt{2}$, Graphs Combinatorics 23 (2007), 713-726]. We study the limit points of the spectral radii of certain families of graphs,...