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The Cartesian product of cycles with small 2-rainbow domination number

Author

Listed:
  • Zofia Stȩpień

    (West Pomeranian University of Technology)

  • Lucjan Szymaszkiewicz

    (Szczecin University)

  • Maciej Zwierzchowski

    (West Pomeranian University of Technology)

Abstract

The concept of 2-rainbow domination of a graph $$G$$ G coincides with the ordinary domination of the prism $$G\Box K_{2}$$ G □ K 2 (see Brešar et al., Taiwan J Math 12:213–225, 2008). Hence $$\gamma _{r2}(C_{m}\Box C_{n})\ge \frac{mn}{3}$$ γ r 2 ( C m □ C n ) ≥ m n 3 . In this paper we give full characterization of graphs $$C_m\Box C_n$$ C m □ C n with $$\gamma _{r2}(C_{m}\Box C_{n}) = \frac{mn}{3}$$ γ r 2 ( C m □ C n ) = m n 3 .

Suggested Citation

  • Zofia Stȩpień & Lucjan Szymaszkiewicz & Maciej Zwierzchowski, 2015. "The Cartesian product of cycles with small 2-rainbow domination number," Journal of Combinatorial Optimization, Springer, vol. 30(3), pages 668-674, October.
    • Handle: RePEc:spr:jcomop:v:30:y:2015:i:3:d:10.1007_s10878-013-9658-0
    DOI: 10.1007/s10878-013-9658-0
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    Cited by:

    1. Hong Gao & Kun Li & Yuansheng Yang, 2019. "The k -Rainbow Domination Number of C n □ C m," Mathematics, MDPI, vol. 7(12), pages 1-19, December.
    2. Hong Gao & Changqing Xi & Yuansheng Yang, 2020. "The 3-Rainbow Domination Number of the Cartesian Product of Cycles," Mathematics, MDPI, vol. 8(1), pages 1-20, January.
    3. Hong Gao & Penghui Wang & Enmao Liu & Yuansheng Yang, 2020. "More Results on Italian Domination in C n □ C m," Mathematics, MDPI, vol. 8(4), pages 1-10, March.
    4. Zepeng Li & Zehui Shao & Jin Xu, 2018. "Weak {2}-domination number of Cartesian products of cycles," Journal of Combinatorial Optimization, Springer, vol. 35(1), pages 75-85, January.
    5. Zepeng Li & Zehui Shao & Shou-jun Xu, 2019. "2-Rainbow domination stability of graphs," Journal of Combinatorial Optimization, Springer, vol. 38(3), pages 836-845, October.

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