Modeling Pedestrian Dynamics on Triangular Grids

Power Domination on Triangular Grids

The concept of power domination emerged from the problem of monitoring electrical systems. Given a graph G and a set S ⊆ V (G), a set M of monitored vertices is built as follows: at first, M contains only the vertices of S and their direct neighbors, and then each time a vertex in M has exactly one neighbor not in M , this neighbor is added to M . The power domination number of a graph G is the...

Transonic Turbulent Flow Computations on Unstructured Triangular Grids

Cutwidth of triangular grids

When the vertices of an n-vertex graph G are numbered by the integers 1 through n, the length of an edge is the difference between the numbers on its endpoints. Two edges overlap if the larger of their lower numbers is less than the smaller of their upper numbers. The bandwidth of G is the minimum, over all numberings, of the maximum length of an edge. The cutwidth of G is the minimum, over all...

Firefighting on square, hexagonal, and triangular grids

In this paper, we consider the firefighter problem on a graph G = (V,E) that is either finite or infinite. Suppose that a fire breaks out at a given vertex v ∈ V . In each subsequent time unit, a firefighter protects one vertex which is not yet on fire, and then the fire spreads to all unprotected neighbors of the vertices on fire. The objective of the firefighter is to save as many vertices as...

Cellular automata modeling for pedestrian dynamics