More Results on the Domination Number of Cartesian Product of Two Directed Cycles
نویسندگان
چکیده
منابع مشابه
On the Signed Domination Number of the Cartesian Product of Two Directed Cycles
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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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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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 G be a graph. A 2-rainbow dominating function (or 2-RDF) of G is a function f from V(G) to the set of all subsets of the set {1,2} such that for a vertex v ∈ V (G) with f(v) = ∅, thecondition $bigcup_{uin N_{G}(v)}f(u)={1,2}$ is fulfilled, wher NG(v) is the open neighborhoodof v. The weight of 2-RDF f of G is the value$omega (f):=sum _{vin V(G)}|f(v)|$. The 2-rainbowd...
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Let Za × Zb be the product of two directed cycles, let Zc be a subgroup of Za, and let Zd be a subgroup of Zb. Also, let A = a c and B =
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ژورنال
عنوان ژورنال: Mathematics
سال: 2019
ISSN: 2227-7390
DOI: 10.3390/math7020210