### Volume 8

n° 1 (2006), pp. 141-158author: | Tiziana Calamoneri |
---|---|

title: | Optimal L(h,k)-Labeling of Regular Grids |

keywords: | L(h,k)-labeling, cellular grids, triangular grids, hexagonal grids, squared grids |

abstract: | The L(h, k)-labeling is an assignment of non negative integer labels to the nodes of a graph such that 'close' nodes have labels which differ by at least k, and 'very close' nodes have labels which differ by at least h. The span of an L(h,k)-labeling is the difference between the largest and the smallest assigned label. We study L(h, k)-labelings of cellular, squared and hexagonal grids, seeking those with minimum span for each value of k and h ≥ k. The L(h,k)-labeling problem has been intensively studied in some special cases, i.e. when k=0 (vertex coloring), h=k (vertex coloring the square of the graph) and h=2k (radio- or λ-coloring) but no results are known in the general case for regular grids. In this paper, we completely solve the L(h,k)-labeling problem on regular grids, finding exact values of the span for each value of h and k; only in a small interval we provide different upper and lower bounds. |

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reference: | Tiziana Calamoneri (2006),
Optimal L(h,k)-Labeling of Regular Grids,
Discrete Mathematics and Theoretical Computer Science 8, pp. 141-158 |

bibtex: | For a corresponding BibTeX entry, please consider our BibTeX-file. |

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Automatically produced on Mon May 15 22:43:32 CEST 2006 by falk