L(j, k)-labeling number of Cartesian product of path and cycle

Qiong Wu, Wai Chee Shiu*, Pak Kiu Sun

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

6 Citations (Scopus)
31 Downloads (Pure)


For positive numbers j and k, an L(j,k)-labeling f of G is an assignment of numbers to vertices of G such that |f(u)−f(v)|≥j if d(u,v)=1, and |f(u)−f(v)|≥k if d(u,v)=2. The span of f is the difference between the maximum and the minimum numbers assigned by f. The L(j,k)-labeling number of G, denoted by λj,k(G), is the minimum span over all L(j,k)-labelings of G. In this article, we completely determine the L(j,k)-labeling number (2j≤k) of the Cartesian product of path and cycle.
Original languageEnglish
Pages (from-to)604-634
Number of pages31
JournalJournal of Combinatorial Optimization
Issue number2
Early online date2 Aug 2014
Publication statusPublished - Feb 2016

Scopus Subject Areas

  • Computer Science Applications
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Theory and Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Cartesian product
  • Cycle
  • L(j, k)-labeling
  • Path


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