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

Author

Listed:
  • Qiong Wu

    (Hong Kong Baptist University
    Tianjin University of Technology and Education)

  • Wai Chee Shiu

    (Hong Kong Baptist University)

  • Pak Kiu Sun

    (Hong Kong Baptist University)

Abstract

For positive numbers $$j$$ j and $$k$$ k , an $$L(j,k)$$ L ( j , k ) -labeling $$f$$ f of $$G$$ G is an assignment of numbers to vertices of $$G$$ G such that $$|f(u)-f(v)|\ge j$$ | f ( u ) - f ( v ) | ≥ j if $$d(u,v)=1$$ d ( u , v ) = 1 , and $$|f(u)-f(v)|\ge k$$ | f ( u ) - f ( v ) | ≥ k if $$d(u,v)=2$$ d ( u , v ) = 2 . The span of $$f$$ f is the difference between the maximum and the minimum numbers assigned by $$f$$ f . The $$L(j,k)$$ L ( j , k ) -labeling number of $$G$$ G , denoted by $$\lambda _{j,k}(G)$$ λ j , k ( G ) , is the minimum span over all $$L(j,k)$$ L ( j , k ) -labelings of $$G$$ G . In this article, we completely determine the $$L(j,k)$$ L ( j , k ) -labeling number ( $$2j\le k$$ 2 j ≤ k ) of the Cartesian product of path and cycle.

Suggested Citation

  • Qiong Wu & Wai Chee Shiu & Pak Kiu Sun, 2016. "$$L(j,k)$$ L ( j , k ) -labeling number of Cartesian product of path and cycle," Journal of Combinatorial Optimization, Springer, vol. 31(2), pages 604-634, February.
    • Handle: RePEc:spr:jcomop:v:31:y:2016:i:2:d:10.1007_s10878-014-9775-4
    DOI: 10.1007/s10878-014-9775-4
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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.
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