Distance-two labelings of digraphs

Gerard J. Chang, Jer Jeong Chen, David Kuo, Sheng Chyang Liaw

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


For positive integers j ≥ k, an L (j, k)-labeling of a digraph D is a function f from V (D) into the set of nonnegative integers such that | f (x) - f (y) | ≥ j if x is adjacent to y in D and | f (x) - f (y) | ≥ k if x is of distance two to y in D. Elements of the image of f are called labels. The L (j, k)-labeling problem is to determine the over(λ, ⇒)j, k-number over(λ, ⇒)j, k (D) of a digraph D, which is the minimum of the maximum label used in an L (j, k)-labeling of D. This paper studies over(λ, ⇒)j, k-numbers of digraphs. In particular, we determine over(λ, ⇒)j, k-numbers of digraphs whose longest dipath is of length at most 2, and over(λ, ⇒)j, k-numbers of ditrees having dipaths of length 4. We also give bounds for over(λ, ⇒)j, k-numbers of bipartite digraphs whose longest dipath is of length 3. Finally, we present a linear-time algorithm for determining over(λ, ⇒)j, 1-numbers of ditrees whose longest dipath is of length 3.

Original languageEnglish
Pages (from-to)1007-1013
Number of pages7
JournalDiscrete Applied Mathematics
Issue number8
StatePublished - 15 Apr 2007


  • Algorithm
  • Digraph
  • Ditree
  • Homomorphism
  • L (j, k)-labeling


Dive into the research topics of 'Distance-two labelings of digraphs'. Together they form a unique fingerprint.

Cite this