On domination of Cartesian product of directed cycles

Michel Mollard (1)

1 IF - Institut Fourier

Let $\gamma(C_m\Box C_n)$ be the domination number of the Cartesian product of directed cycles $C_m$ and $C_n$ for $m,n\geq2$. Shaheen [] and Liu and al.[ ], [ ] determined the value of $\gamma(C_m\Box C_n)$ when $m \leq 6$ and when both $m$ and $n$ $\equiv 0$ $(mod\: 3)$. In this article we give, in general, the value of $\gamma(C_m\Box C_n)$ when $m\equiv 2$ $(mod\: 3)$ and improve the known lower bound for most of the remaining cases. We also disprove the conjectured formula for the case $m$ $\equiv 0$ $(mod\: 3)$ appearing in \cite{}

Mots clés: Graph; Domination; Cartesian Product

Domaines: Combinatoire [math.CO]

Michel Mollard. On domination of Cartesian product of directed cycles. 2011. ⟨hal-00576481v3⟩