- Lattice graph
The terms lattice graph, mesh graph, or grid graph refer to a number of categories of graphs whose drawing corresponds to some grid/mesh/lattice, i.e., its vertices correspond to the nodes of the mesh and its edges correspond to the ties between the nodes.
Square grid graph
A common type of a lattice graph (known under different names, such as square grid graph) is the graph whose vertices correspond to the points in the plane with integer coordinates, x-coordinates being in the range 0,..., n, y-coordinates being in the range 1,...m, and two vertices are connected by an edge whenever the corresponding points are at distance 1. In other words, it is a unit distance graph for the described point set.
A square grid graph is a Cartesian product of graphs, namely, of two path graphs with n and m edges. Since a path graph is a median graph, the latter fact implies that the square grid graph is also a median graph. All grid graphs are bipartite.
A triangular grid graph is a graph that corresponds to a triangular grid.
A Hanan grid graph for a finite set of points in the plane is produced by the grid obtained by intersections of all vertical and horizontal lines through each point of the set.
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