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Mathematics 2019, 7(2), 210; https://doi.org/10.3390/math7020210

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

1
School of Geophysics, Chengdu University of Technology, Chengdu 610059, China
2
School of Information Science and Engineering, Chengdu University, Chengdu 610106, China
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Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China
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School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China
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Faculty of Mechanical Engineering, University of Ljubljana, SI-1000 Ljubljana, Slovenia
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Institute of Mathematics, Physics and Mechanics, SI-1000 Ljubljana, Slovenia
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Faculty of Natural Sciences and Mathematics, University of Maribor, SI-2000 Maribor, Slovenia
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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
(This article belongs to the Special Issue Graph-Theoretic Problems and Their New Applications)
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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. 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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