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

Author

Listed:
  • Qiong Wu

    (Hong Kong Baptist University)

  • Wai Chee Shiu

    (Hong Kong Baptist University)

  • Pak Kiu Sun

    (Hong Kong Baptist University)

Abstract

Let j, k and m be positive numbers, a circular m-L(j,k)-labeling of a graph G is a function f:V(G)→[0,m) such that |f(u)−f(v)| m ≥j if u and v are adjacent, and |f(u)−f(v)| m ≥k if u and v are at distance two, where |a−b| m =min{|a−b|,m−|a−b|}. The minimum m such that there exist a circular m-L(j,k)-labeling of G is called the circular L(j,k)-labeling number of G and is denoted by σ j,k (G). In this paper, for any two positive numbers j and k with j≤k, we give some results about the circular L(j,k)-labeling number of direct product of path and cycle.

Suggested Citation

  • Qiong Wu & Wai Chee Shiu & Pak Kiu Sun, 2014. "Circular L(j,k)-labeling number of direct product of path and cycle," Journal of Combinatorial Optimization, Springer, vol. 27(2), pages 355-368, February.
    • Handle: RePEc:spr:jcomop:v:27:y:2014:i:2:d:10.1007_s10878-012-9520-9
    DOI: 10.1007/s10878-012-9520-9
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    References listed on IDEAS

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    1. Jerrold R. Griggs & Xiaohua Teresa Jin, 2007. "Recent progress in mathematics and engineering on optimal graph labellings with distance conditions," Journal of Combinatorial Optimization, Springer, vol. 14(2), pages 249-257, October.
    2. Xiaohua Teresa Jin & Roger K. Yeh, 2005. "Graph distance‐dependent labeling related to code assignment in computer networks," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(2), pages 159-164, March.
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