Lattice graph

In graph theory, a lattice graph, mesh graph, or grid graph is a graph whose drawing, embedded in some Euclidean space ‍${\displaystyle \mathbb {R} ^{n}}$‍, forms a regular tiling. This implies that the group of bijective transformations that send the graph to itself is a lattice in the group-theoretical sense.

Typically, no clear distinction is made between such a graph in the more abstract sense of graph theory, and its drawing in space (often the plane or 3D space). This type of graph may more shortly be called just a lattice, mesh, or grid. Moreover, these terms are also commonly used for a finite section of the infinite graph, as in "an 8 × 8 square grid".

The term lattice graph has also been given in the literature to various other kinds of graphs with some regular structure, such as the Cartesian product of a number of complete graphs.^[1]