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The domination number of Cartesian product of two directed paths

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  • Michel Mollard

    (Institut Fourier)

Abstract

Let γ(P m □P n ) be the domination number of the Cartesian product of directed paths P m and P n for m,n≥2. Liu et al. in (J. Comb. Optim. 22(4):651–662, 2011) determined the value of γ(P m □P n ) for arbitrary n and m≤6. In this work we give the exact value of γ(P m □P n ) for any m,n and exhibit dominating sets of minimum cardinality.

Suggested Citation

  • Michel Mollard, 2014. "The domination number of Cartesian product of two directed paths," Journal of Combinatorial Optimization, Springer, vol. 27(1), pages 144-151, January.
    • Handle: RePEc:spr:jcomop:v:27:y:2014:i:1:d:10.1007_s10878-012-9494-7
    DOI: 10.1007/s10878-012-9494-7
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    References listed on IDEAS

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    1. Juan Liu & Xindong Zhang & Jixiang Meng, 2011. "On domination number of Cartesian product of directed paths," Journal of Combinatorial Optimization, Springer, vol. 22(4), pages 651-662, November.
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    Cited by:

    1. Fu-Tao Hu & Moo Young Sohn & Xue-gang Chen, 2016. "Total and paired domination numbers of $$C_m$$ C m bundles over a cycle $$C_n$$ C n," Journal of Combinatorial Optimization, Springer, vol. 32(2), pages 608-625, August.
    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.

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    1. Fu-Tao Hu & Moo Young Sohn & Xue-gang Chen, 2016. "Total and paired domination numbers of $$C_m$$ C m bundles over a cycle $$C_n$$ C n," Journal of Combinatorial Optimization, Springer, vol. 32(2), pages 608-625, August.

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