Golden-Ten is an observation game in which players try to predict the outcome of the motion of a ball rolling down the surface of a drum.This paper describes the motion of the ball as a stochastic model, based on a deterministic, mechanical model.To this end, the motion is split into several...

We study the connected regular graphs with four distinct eigenvalues. Properties and feasibility conditions of the eigenvalues are found. Several examples, constructions and characterizations are given, as well as some uniqueness and nonexistence results.

We give a bound on the sizes of two sets of vertices at a given minimum distance (a separated pair of subgraphs) in a graph in terms of polynomials and the spectrum of the graph. We find properties of the polynomial optimizing the bound. Explicit bounds on the number of vertices at maximal...

We give several old and some new applications of eigenvalue interlacing to matrices associated to graphs. Bounds are obtained for characteristic numbers of graphs, such as the size of a maximal (co)clique, the chromatic number, the diameter and the bandwidth in terms of the eigenvalues of the...

We characterize the distance-regular graphs with diameter three by giving an expression for the number of vertices at distance two from each given vertex, in terms of the spectrum of the graph.

A graph G has constant u = u(G) if any two vertices that are not adjacent have u common neighbours. G has constant u and u if G has constant u = u(G), and its complement G has constant u = u(G). If such a graph is regular, then it is strongly regular, otherwise precisely two vertex degrees...