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 correponding points are at distance 1. In other words, it is a unit distance graph for the described point set.
A path graph may also be considered to be a grid graph on the grid n times 1. A 2x2 grid graph is a 4-cycle.
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.