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 journalArticlepeer-review

6 Citations (Scopus)
2 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
Publication statusPublished - 1 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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