More Results on the Domination Number of Cartesian Product of Two Directed Cycles
School of Geophysics, Chengdu University of Technology, Chengdu 610059, China
School of Information Science and Engineering, Chengdu University, Chengdu 610106, China
Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China
School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China
Faculty of Mechanical Engineering, University of Ljubljana, SI-1000 Ljubljana, Slovenia
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
Author to whom correspondence should be addressed.
Received: 12 December 2018 / Revised: 12 February 2019 / Accepted: 21 February 2019 / Published: 24 February 2019
denote the domination number of a digraph D
denote the Cartesian product of
, the directed cycles of length
. Liu et al. obtained the exact values of
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
[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
[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
up to 21. Moreover, the exact values of
up to 31 are determined.
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
Share & Cite This Article
MDPI and ACS Style
Ye, A.; Miao, F.; Shao, Z.; Liu, J.-B.; Žerovnik, J.; Repolusk, P. More Results on the Domination Number of Cartesian Product of Two Directed Cycles. Mathematics 2019, 7, 210.
Ye A, Miao F, Shao Z, Liu J-B, Žerovnik J, Repolusk P. More Results on the Domination Number of Cartesian Product of Two Directed Cycles. Mathematics. 2019; 7(2):210.
Ye, Ansheng; Miao, Fang; Shao, Zehui; Liu, Jia-Bao; Žerovnik, Janez; Repolusk, Polona. 2019. "More Results on the Domination Number of Cartesian Product of Two Directed Cycles." Mathematics 7, no. 2: 210.
Show more citation formats
Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.
[Return to top]
For more information on the journal statistics, click here
Multiple requests from the same IP address are counted as one view.