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More Results on the Domination Number of Cartesian Product of Two Directed Cycles

Author

Listed:
  • Ansheng Ye

    (School of Geophysics, Chengdu University of Technology, Chengdu 610059, China
    School of Information Science and Engineering, Chengdu University, Chengdu 610106, China)

  • Fang Miao

    (School of Geophysics, Chengdu University of Technology, Chengdu 610059, China
    School of Information Science and Engineering, Chengdu University, Chengdu 610106, China)

  • Zehui Shao

    (Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China)

  • Jia-Bao Liu

    (School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China)

  • Janez Žerovnik

    (Faculty of Mechanical Engineering, University of Ljubljana, SI-1000 Ljubljana, Slovenia
    Institute of Mathematics, Physics and Mechanics, SI-1000 Ljubljana, Slovenia)

  • Polona Repolusk

    (Institute of Mathematics, Physics and Mechanics, SI-1000 Ljubljana, Slovenia
    Faculty of Natural Sciences and Mathematics, University of Maribor, SI-2000 Maribor, Slovenia
    Faculty of Information Studies, P.O. Box 603, 8000 Novo Mesto, Slovenia)

Abstract

Let γ ( D ) denote the domination number of a digraph D and let C m □ C n denote the Cartesian product of C m and C n , the directed cycles of length n ≥ m ≥ 3 . Liu et al. obtained the exact values of γ ( C m □ C n ) for m up to 6 [Domination number of Cartesian products of directed cycles, Inform. Process. Lett. 111 (2010) 36–39]. Shao et al. determined the exact values of γ ( C m □ C n ) for m = 6 , 7 [On the domination number of Cartesian product of two directed cycles, Journal of Applied Mathematics, Volume 2013, Article ID 619695]. Mollard obtained the exact values of γ ( C m □ C n ) for m = 3 k + 2 [M. Mollard, On domination of Cartesian product of directed cycles: Results for certain equivalence classes of lengths, Discuss. Math. Graph Theory 33(2) (2013) 387–394.]. In this paper, we extend the current known results on C m □ C n with m up to 21. Moreover, the exact values of γ ( C n □ C n ) with n up to 31 are determined.

Suggested Citation

  • Ansheng Ye & Fang Miao & Zehui Shao & Jia-Bao Liu & Janez Žerovnik & Polona Repolusk, 2019. "More Results on the Domination Number of Cartesian Product of Two Directed Cycles," Mathematics, MDPI, vol. 7(2), pages 1-9, February.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:2:p:210-:d:208727
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    References listed on IDEAS

    as
    1. Zehui Shao & Enqiang Zhu & Fangnian Lang, 2013. "On the Domination Number of Cartesian Product of Two Directed Cycles," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-7, December.
    2. Zehui Shao & Jin Xu & S. M. Sheikholeslami & Shaohui Wang, 2018. "The Domination Complexity and Related Extremal Values of Large 3D Torus," Complexity, Hindawi, vol. 2018, pages 1-8, July.
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