Labelling graphs with a condition at distance 2
SIAM Journal on Discrete Mathematics
L(h,1)-labeling subclasses of planar graphs
Journal of Parallel and Distributed Computing
New bounds for the L(h, k) number of regular grids
International Journal of Mobile Network Design and Innovation
Graph labeling and radio channel assignment
Journal of Graph Theory
Real Number Channel Assignments for Lattices
SIAM Journal on Discrete Mathematics
The Computer Journal
On n-fold L(j,k)-and circular L(j,k)-labelings of graphs
Discrete Applied Mathematics
Distance two edge labelings of lattices
Journal of Combinatorial Optimization
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Suppose G is a graph. Let u be a vertex of G. A vertex v is called an i-neighbor of u if d"G(u,v)=i. A 1-neighbor of u is simply called a neighbor of u. Let s and t be two nonnegative integers. Suppose f is an assignment of nonnegative integers to the vertices of G. If the following three conditions are satisfied, then f is called an (s,t)-relaxed L(2,1)-labeling of G: (1) for any two adjacent vertices u and v of G, f(u)f(v); (2) for any vertex u of G, there are at most s neighbors of u receiving labels from {f(u)-1,f(u)+1}; (3) for any vertex u of G, the number of 2-neighbors of u assigned the label f(u) is at most t. The minimum span of (s,t)-relaxed L(2,1)-labelings of G is called the (s,t)-relaxed L(2,1)-labeling number of G, denoted by @l"2","1^s^,^t(G). It is clear that @l"2","1^0^,^0(G) is the so-called L(2,1)-labeling number of G. In this paper, the (s,t)-relaxed L(2,1)-labeling number of the square lattice is determined for each pair of two nonnegative integers s and t. And this provides a series of channel assignment schemes for the corresponding channel assignment problem on the square lattice.