The L(2, 1)-Labeling Problem on Oriented Regular Grids

Details The L(2, 1)-Labeling Problem on Oriented Regular Grids The L(2, 1)-Labeling Problem on Oriented Regular Grids

2009-05-12

arxiv.org/abs/0905.1780v2

Computer Science

Discrete Mathematics

The content of this paper has been presented to ICTCS 2009, 28-30 September, Cremona, Italy. This updated version is a longer

Scientific paper

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 $\lambda$.

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