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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.
Mathematics 2019, 7(2), 210;
Received: 12 December 2018 / Revised: 12 February 2019 / Accepted: 21 February 2019 / Published: 24 February 2019
(This article belongs to the Special Issue Graph-Theoretic Problems and Their New Applications)
PDF [1207 KB, uploaded 25 February 2019]


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. View Full-Text
Keywords: domination number; Cartesian product; directed cycle domination number; Cartesian product; directed cycle

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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.

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