%0 Journal Article
%T Optimal L(h,k)-Labeling of Regular Grids
%A Tiziana Calamoneri
%J Discrete Mathematics & Theoretical Computer Science
%D 2006
%I Discrete Mathematics & Theoretical Computer Science
%X 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 ¡Ý 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 ¦Ë-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.
%U http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/506