  The L(2, 1)-labeling of a digraph G is a function f from the node set of $G$
to the set of all nonnegative integers such that $|f(x)-f(y)| \geq 2$ if $x$
and $y$ are at distance 1, and $f(x)=f(y)$ if $x$ and $y$ are at distance 2,
where the distance from vertex $x$ to vertex $y$ is the length of a shortest
dipath from $x$ to $y$. The minimum of the maximum used label over all $L(2,
1)$-labelings of $G$ is called $\lambda(G)$. In this paper we study the L(2,
1)-labeling problem on squared, triangular and hexagonal grids and for them we
compute the exact values of $\lambda$.
