Cutwidth of 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...

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...

Hamiltonian Cycles in Triangular Grids

We study the Hamiltonian Cycle problem in graphs induced by subsets of the vertices of the tiling of the plane with equilateral triangles. By analogy with grid graphs we call such graphs triangular grid graphs. Following the analogy, we define the class of solid triangular grid graphs. We prove that the Hamiltonian Cycle problem is NPcomplete for triangular grid graphs. We show that with the ex...

Transonic Turbulent Flow Computations on Unstructured Triangular Grids

Generalised Triangular Grids in Digital Geometry

The hexagonal and the triangular grids are duals of each other. These two grids are the first and second ones in the family of triangular grids (we can call them as oneand two-planes triangular grids). This family comes from the mapping their points to Z3. Their symmetric properties are triangular. The next grid is the three-planes triangular grid, which looks like the mix of them. In this pape...