The domination number of Cartesian product of two directed paths

Michel Mollard (1)

1 IF - Institut Fourier

Let $\gamma(P_m\Box P_n)$ be the domination number of the Cartesian product of directed paths $P_m$ and $P_n$ for $m,n\geq2$. In this journal J. Liu, X.D. Zhang, X. Chen, J.Meng (On Domination number of Cartesian product of directed paths, \emph{J. Comb. Optim.}, \textbf{ 22(4)} 651-662 (2011)) determined the value of $\gamma(P_m\Box P_n)$ for arbitrary $n$ and $m \leq 6$. In this work we give the exact value of $\gamma(P_m\Box P_n)$ for any $m,n$ and exhibit minimum dominating sets.

Mots clés: Directed graph; digraph; Cartesian product; Domination number; Paths

Domaines: Combinatoire [math.CO]

Michel Mollard. The domination number of Cartesian product of two directed paths. Journal of Combinatorial Optimization, 2014, 27 (1), pp.144-151. ⟨hal-00655403⟩