The Cartesian product of cycles with small 2-rainbow domination number
Zofia Stępień, Lucjan Szymaszkiewicz, Maciej Zwierzchowski · Journal of Combinatorial Optimization · 2013
The concept of 2-rainbow domination of a graph $$G$$ coincides with the ordinary domination of the prism $$G\Box K_{2}$$ (see Brešar et al., Taiwan J Math 12:213–225, 2008). Hence $$\gamma _{r2}(C_{m}\Box C_{n})\ge \frac{mn}{3}$$ . In this paper we give full characterization of graphs $$C_m\Box C_n$$ with $$\gamma _{r2}(C_{m}\Box C_{n}) = \frac{mn}{3}$$ .