Domination number of Cartesian products of directed cycles

Authors:
Xindong Zhang;Juan Liu;Xing Chen;Jixiang Meng
Affiliations:
College of Mathematics Sciences, Xinjiang Normal University, Urumqi, Xinjiang, 830054, PR China;College of Mathematics Sciences, Xinjiang Normal University, Urumqi, Xinjiang, 830054, PR China and College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang, 830046, PR Ch ...;College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang, 830046, PR China;College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang, 830046, PR China
Venue:
Information Processing Letters
Year:
2010

Citing 6
Cited 3

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Abstract

Let @c(G) denote the domination number of a digraph G and let C"m@?C"n denote the Cartesian product of C"m and C"n, the directed cycles of length m,n=2. In Liu et al. (2010) [11], we determined the exact values of @c(C"m@?C"n) when m=2,3,4. In this paper, we give a lower and upper bounds for @c(C"m@?C"n). Furthermore, we prove a necessary and sufficient conditions for C"m@?C"n to have an efficient dominating set. Also, we determine the exact values: @c(C"5@?C"n)=2n; @c(C"6@?C"n)=2n if n=0(mod 3), otherwise, @c(C"6@?C"n)=2n+2; @c(C"m@?C"n)=mn3 if m=0(mod 3) and n=0(mod 3).