On the Domination of Cartesian Product of Directed Cycles: Results for Certain Equivalence Classes of Lengths

Discussiones Mathematicae Graph Theory

Mollard Michel¹ 

[1] CNRS Université Joseph Fourier Institut Fourier 100, rue des Maths 38402 St Martin d’Hères Cedex France;

关键词: directed graph;    cartesian product;    domination number;    directed cycle;   

DOI  :  10.7151/dmgt.1668

来源: DOAJ

【 摘 要 】

Let (−→ Cm2−→ Cn) be the domination number of the Cartesian product of directed cycles −→ Cm and −→ Cn for m, n ≥ 2. Shaheen [13] and Liu et al. ([11], [12]) determined the value of (−→ Cm2−→ Cn) when m ≤ 6 and [12] when both m and n ≡ 0(mod 3). In this article we give, in general, the value of (−→ Cm2−→ Cn) when m ≡ 2(mod 3) and improve the known lower bounds for most of the remaining cases. We also disprove the conjectured formula for the case m ≡ 0(mod 3) appearing in [12].

【 授权许可】

Unknown