Labelling graphs with a condition at distance 2
SIAM Journal on Discrete Mathematics
Labeling Chordal Graphs: Distance Two Condition
SIAM Journal on Discrete Mathematics
On the $\lambda$-Number of $Q_n$ and Related Graphs
SIAM Journal on Discrete Mathematics
Code assignment for hidden terminal interference avoidance in multihop packet radio networks
IEEE/ACM Transactions on Networking (TON)
The $L(2,1)$-Labeling Problem on Graphs
SIAM Journal on Discrete Mathematics
Assigning codes in wireless networks: bounds and scaling properties
Wireless Networks
On L(d, 1)-labelings of graphs
Discrete Mathematics
Frequency Channel Assignment on Planar Networks
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Channel Assignment with Separation for Interference Avoidance in Wireless Networks
IEEE Transactions on Parallel and Distributed Systems
L(h,1)-labeling subclasses of planar graphs
Journal of Parallel and Distributed Computing
L(2, 1)-labeling of strong products of cycles
Information Processing Letters
Graph labellings with variable weights, a survey
Discrete Applied Mathematics
On (s,t)-relaxed L (2,1)-labelings of the square lattice
Information Processing Letters
Multiple L(j,1)-labeling of the triangular lattice
Journal of Combinatorial Optimization
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For any non-negative real values h and k, an L(h, k)-labellingof a graph G = (V,E) is a function L : V → R such that |L(u)− L(v)| ≥ h if (u, v) ∈ E and |L(u) − L(v)|≥ k if there exists w ∈ V such that (u,w) ∈ E and (w,v) ∈ E. The span of an L(h, k)-labelling is the differencebetween the largest and the smallest value of L. We denote byλh,k(G) the smallest real λ such that graph G has anL(h, k)-labelling of span λ. The aim of the L(h,k)-labelling problem is to satisfy the distance constraints usingthe minimum span. In this paper, we study the L (h, k)-labellingproblem on regular grids of degree 3, 4 and 6 for those values of hand k whose λh,k is either not known or not tight. We alsoinitiate the study of the problem for grids of degree 8. For allconsidered grids, in some cases we provide exact results, while inthe other ones we give very close upper and lower bounds.