On domination of Cartesian product of directed cycles: Results for certain equivalence classes of lengths
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چکیده
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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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 remai...
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Let D be a finite simple directed graph with vertex set V(D) and arc set A(D). A function ( ) { } − : 1,1 f V D → is called a signed dominating function (SDF) if [ ] ( ) 1 D f N v − ≥ for each vertex v V ∈ . The weight ( ) f ω of f is defined by ( ) ∑ v V f v ∈ . The signed domination number of a digraph D is ( ) ( ) { } γ ω = min is an SDF of s D f f D . Let Cm × Cn denotes the cartesian produ...
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The domination number of Cartesian product of two directed paths
4 Let γ(Pm2Pn) be the domination number of the Cartesian product of directed paths Pm and Pn for m,n ≥ 2. In [13] Liu and al. determined the value of γ(Pm2Pn) 6 for arbitrary n and m ≤ 6. In this work we give the exact value of γ(Pm2Pn) for any m,n and exhibit minimum dominating sets. 8 AMS Classification[2010]:05C69,05C38. 10
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ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2013
ISSN: 1234-3099,2083-5892
DOI: 10.7151/dmgt.1668