Labeling trees with a condition at distance two

For positive integers j⩾ k, an L( j, k)-labeling of graph G is an integer labeling of V( G) such that adjacent vertices receive labels which differ by at least j, and vertices that are distance two apart receive labels which differ by at least k. The λ j, k -number of G is the minimum span over the...

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Bibliographic Details
Published in:Discrete mathematics 2003-07, Vol.269 (1), p.127-148
Main Authors: Georges, John P., Mauro, David W.
Format: Article
Language:English
Subjects:
Combinatorics
Combinatorics. Ordered structures
Exact sciences and technology
Graph theory
Infinite regular tree
Mathematics
Sciences and techniques of general use
Vertex labeling
λj, k-labeling
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Summary:For positive integers j⩾ k, an L( j, k)-labeling of graph G is an integer labeling of V( G) such that adjacent vertices receive labels which differ by at least j, and vertices that are distance two apart receive labels which differ by at least k. The λ j, k -number of G is the minimum span over the L( j, k)-labelings of G. In this paper, we derive the λ j, k -number of the infinite regular tree. For x= j/ k, we also introduce a rational variation λ x ( G) of λ j, k ( G), and provide a proof that λ x ( G) is continuous.
ISSN:0012-365X
1872-681X
DOI:10.1016/S0012-365X(02)00750-1