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

Ansheng Ye, Fang Miao, Zehui Shao, Jia-Bao Liu, Janez Žerovnik and Polona Repolusk
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Ansheng Ye: School of Geophysics, Chengdu University of Technology, Chengdu 610059, China
Fang Miao: School of Geophysics, Chengdu University of Technology, Chengdu 610059, 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
Polona Repolusk: Institute of Mathematics, Physics and Mechanics, SI-1000 Ljubljana, Slovenia

Mathematics, 2019, vol. 7, issue 2, 1-9

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.

Keywords: domination number; Cartesian product; directed cycle (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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