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

Author:

Calamoneri Tiziana

Abstract

International audience 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.

Publisher

Centre pour la Communication Scientifique Directe (CCSD)

Subject

Discrete Mathematics and Combinatorics,General Computer Science,Theoretical Computer Science

Cited by 5 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Multiple L(j,1)-labeling of the triangular lattice;Journal of Combinatorial Optimization;2012-09-18

2. Graph labellings with variable weights, a survey;Discrete Applied Mathematics;2009-06

3. Optimal Real Number Graph Labellings of a Subfamily of Kneser Graphs;SIAM Journal on Discrete Mathematics;2009-01

4. A General Approach to L(h,k)-Label Interconnection Networks;Journal of Computer Science and Technology;2008-07

5. Bounds for the Real Number Graph Labellings and Application to Labellings of the Triangular Lattice;SIAM Journal on Discrete Mathematics;2008-01

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