The problem of finding a maximin Latin hypercube design in two dimensions can be described as positioning n non-attacking rooks on an n x n chessboard such that the minimal distance between pairs of rooks is maximized. Maximin Latin hypercube designs are important for the approximation and...

We construct distance-regular graphs with the same-classical-parameters as the Grassman graphs on the e-dimensional subspaces of a (2e+1)-dimensional space over an arbitrary finite field. This provides the first known family of non-transitive distance-regular graphs with unbounded diameter

The design of computer experiments is an important step in black box evaluation and optimization processes. When dealing with multiple black box functions the need often arises to construct designs for all black boxes jointly, instead of individually. These so-called nested designs are used to...

In this and a sequel paper, we study combinatorial designs whose incidence matrix has two distinct singular values. These generalize 2-(v, k, lambda) designs, and include partial geometric designs and uniform multiplicative designs. Here, we study the latter, which are precisely the nonsingular...

In this and an earlier paper [17], we study combinatorial designs whose incidence matrix has two distinct singular values. These generalize (v, k, lambda) designs, and include uniform multiplicative designs and partial geometric designs. Here, we study the latter, which are precisely the designs...

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,...

Latin hypercube designs (LHDs) play an important role when approximating computer simulation models.To obtain good space-filling properties, the maximin criterion is frequently used. Unfortunately, constructing maximin LHDs can be quite time-consuming when the number of dimensions and design...

In the area of computer simulation, Latin hypercube designs play an important role. In this paper the classes of maximin and Audze-Eglais Latin hypercube designs are considered. Up to now only several two-dimensional designs and a few higher dimensional designs for these classes have been...

Let J be the all-ones matrix, and let A denote the adjacency matrix of a graph. An old result of Johnson and Newman states that if two graphs are cospectral with respect to yJ - A for two distinct values of y, then they are cospectral for all y. Here we will focus on graphs cospectral with...

The spectral radius of a graph (i.e., the largest eigenvalue of its corresponding adjacency matrix) plays an important role in modeling virus propagation in networks.In fact, the smaller the spectral radius, the larger the robustness of a network against the spread of viruses.Among all connected...