Discrete Mathematics & Theoretical Computer Science, Vol 8 (2006)

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DMTCS vol 8 no 1 (2006), pp. 141-158


Volume 8

n° 1 (2006), pp. 141-158

author: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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