نتایج جستجو برای: minus dominating function
تعداد نتایج: 1231035 فیلتر نتایج به سال:
A Roman dominating function on a graph G = (V, E) is a function f : V → {0, 1, 2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. The weight of a Roman dominating function is the value f(V ) = ∑ u∈V f(u). The minimum weight of a Roman dominating function on a graph G is called the Roman domination number of G. In this pape...
A Roman dominating function on a graph G is a function f : V (G) → {0, 1, 2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. The weight of a Roman dominating function is the value f(V (G)) = ∑ u∈V (G) f(u). The Roman domination number of G, γR(G), is the minimum weight of a Roman dominating function on G. In this paper, we...
A Roman dominating function on a graph G is a function f : V (G) → {0, 1, 2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. The weight of a Roman dominating function is the value f(V (G)) = ∑ u∈V (G) f(u). The Roman domination number γR(G) of G is the minimum weight of a Roman dominating function on G. In this paper, we s...
Given an undirected graph G = (V,E) and a weight function w : E → R, the Minimum Dominating Tree problem asks to find a minimum weight sub-tree of G, T = (U,F ), such that every v ∈ V \U is adjacent to at least one vertex in U . The special case when the weight function is uniform is known as the Minimum Connected Dominating Set problem. Given an undirected graph G = (V,E) with some subsets of ...
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...
A Roman dominating function on a graph G is a function f : V (G) → {0, 1, 2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. The weight of a Roman dominating function is the value f(V (G)) =
For a positive integer k, a total {k}-dominating function of a graph G without isolated vertices is a function f from the vertex set V (G) to the set {0, 1, 2, . . . , k} such that for any vertex v ∈ V (G), the condition ∑ u∈N(v) f(u) ≥ k is fulfilled, where N(v) is the open neighborhood of v. The weight of a total {k}-dominating function f is the value ω(f) = ∑ v∈V f(v). The total {k}-dominati...
Let $G$ be a simple graph with vertex set $V$. A double Roman dominating function (DRDF) on $G$ is a function $f:Vrightarrow{0,1,2,3}$ satisfying that if $f(v)=0$, then the vertex $v$ must be adjacent to at least two vertices assigned $2$ or one vertex assigned $3$ under $f$, whereas if $f(v)=1$, then the vertex $v$ must be adjacent to at least one vertex assigned $2$ or $3$. The weight of a DR...
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