Grid graph

Grid graph --- граф решетки.

A grid graph is a finite node-induced subgraph of the infinite grid [math]\displaystyle{ G^{\infty} }[/math]. The node set of [math]\displaystyle{ G^{\infty} }[/math] consists of all points of the plane with integer coordinates. Two nodes are connected iff their Euclidean distance is equal to 1. A grid graph is completely specified by its node set. A grid graph [math]\displaystyle{ R(m,n) }[/math] is call rectangular if its node set [math]\displaystyle{ V(R(m,n)) = \{v: \; 1 \leq v_{x} \leq m, \; 1 \leq v_{y} \leq n\} }[/math], where [math]\displaystyle{ v_{x} }[/math] and [math]\displaystyle{ v_{y} }[/math] are the [math]\displaystyle{ x }[/math] and [math]\displaystyle{ y }[/math] coordinates of [math]\displaystyle{ v }[/math] respectively.

The other name is Lattice graph.