Pair labellings with given distance
SIAM Journal on Discrete Mathematics
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
The $L(2,1)$-Labeling Problem on Graphs
SIAM Journal on Discrete Mathematics
On L(d, 1)-labelings of graphs
Discrete Mathematics
Distance-two labelings of graphs
European Journal of Combinatorics
Labeling trees with a condition at distance two
Discrete Mathematics
L(h,1)-labeling subclasses of planar graphs
Journal of Parallel and Distributed Computing
Real Number Graph Labellings with Distance Conditions
SIAM Journal on Discrete Mathematics
A bound on the chromatic number of the square of a planar graph
Journal of Combinatorial Theory Series B
The L(h, k)-Labelling Problem: A Survey and Annotated Bibliography
The Computer Journal
Real Number Channel Assignments for Lattices
SIAM Journal on Discrete Mathematics
Computational Complexity of the Distance Constrained Labeling Problem for Trees (Extended Abstract)
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
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Let G be a graph. For two vertices u and v in G, we denote d(u,v) the distance between u and v. Let j,k be positive integers with j=k. An L(j,k)-labelling for G is a function f:V(G)-{0,1,2,...} such that for any two vertices u and v, |f(u)-f(v)| is at least j if d(u,v)=1; and is at least k if d(u,v)=2. The span of f is the difference between the largest and the smallest numbers in f(V). The @l"j","k-number for G, denoted by @l"j","k(G), is the minimum span over all L(j,k)-labellings of G. We introduce a new parameter for a tree T, namely, the maximum ordering-degree, denoted by M(T). Combining this new parameter and the special family of infinite trees introduced by Chang and Lu (2003) [3], we present upper and lower bounds for @l"j","k(T) in terms of j, k, M(T), and @D(T) (the maximum degree of T). For a special case when j=@D(T)k, the upper and the lower bounds are k apart. Moreover, we completely determine @l"j","k(T) for trees T with j=M(T)k.