On the domination of Cartesian product of directed cycles: Results for certain equivalence classes of 2 lengths
نویسنده
چکیده
Let γ( −→ Cm2 −→ Cn) be the domination number of the Cartesian product of directed 6 cycles −→ Cm and −→ Cn for m,n ≥ 2. Shaheen [13] and Liu et al.([11], [12]) determined the value of γ( −→ Cm2 −→ Cn) when m ≤ 6 and [12] when both m and n ≡ 0 (mod 3). In 8 this article we give, in general, the value of γ( −→ Cm2 −→ Cn) when m ≡ 2 (mod 3) and improve the known lower bounds for most of the remaining cases. We also disprove 10 the conjectured formula for the case m ≡ 0 (mod 3) appearing in [12]. 12 AMS Classification[2010]:05C69,05C38. 14
منابع مشابه
On the Domination of Cartesian Product of Directed Cycles: Results for Certain Equivalence Classes of Lengths
Let γ( −→ 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 γ( −→ 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 γ(−→ Cm2 −→ Cn) when m ≡ 2(mod 3) and improve the known lower bounds for most of the remaining c...
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