Journal article
Distance-two labellings of Hamming graphs
GJ Chang, C Lu, S Zhou
Discrete Applied Mathematics | Published : 2009
Abstract
Let j ≥ k ≥ 0 be integers. An ℓ-L (j, k)-labelling of a graph G = (V, E) is a mapping φ{symbol} : V → {0, 1, 2, ..., ℓ} such that | φ{symbol} (u) - φ{symbol} (v) | ≥ j if u, v are adjacent and | φ{symbol} (u) - φ{symbol} (v) | ≥ k if they are distance two apart. Let λj, k (G) be the smallest integer ℓ such that G admits an ℓ-L (j, k)-labelling. Define over(λ, -)j, k (G) to be the smallest ℓ if G admits an ℓ-L (j, k)-labelling with φ{symbol} (V) = {0, 1, 2, ..., ℓ} and ∞ otherwise. An ℓ-cyclic L (j, k)-labelling is a mapping φ{symbol} : V → Zℓ such that | φ{symbol} (u) - φ{symbol} (v) |ℓ ≥ j if u, v are adjacent and | φ{symbol} (u) - φ{symbol} (v) |ℓ ≥ k if they are distance two apart, where ..
View full abstractGrants
Awarded by Australian Research Council
Funding Acknowledgements
[ "First author was supported in part by the National Science Council under the grant NSC95-2115-M-002-013-MY3.", "Second author was supported by NNSF grants (NNSFC 10301010 and 60673048) from People's Republic of China and by the National Science Council of the Republic of China under a postdoctoral fellowship program from March 2001 to October 2002. He was also supported by a Shanghai Leading Academic Discipline Project (No. B407).", "Third author was supported by a Discovery Project Grant (DP0558677) of the Australian Research Council. Part of the work was initiated during a visit to the National Taiwan University in June 2002 under the scheme \"Scientific Visits to Taiwan\" supported by the Australian Academy of Science and the National Science Council of the Republic of China." ]