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A set S of vertices of a graph G = (V, E) is a dominating set if every vertex of V (G) \ S is adjacent to some vertex in S. The domination number γ (G) is the minimum cardinality of a dominating set of G. The domination subdivision number sd γ (G) is the minimum number of edges that must be subdivided in order to increase the domination number. Velammal… (More)

- H. ARAM
- 2011

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)… (More)

- H. Aram, M. Atapour, L. Volkmann
- 2011

Let D be a finite and simple digraph with vertex set V (D), and let f : V (D) → {−1, 1} be a two-valued function. If k ≥ 1 is an integer and x∈N − [v] f (x) ≥ k for each v ∈ V (D), where N − [v] consists of v and all vertices of D from which arcs go into v, then f is a signed k-dominating function on D. A set {f1, f2,. .. , f d } of distinct signed… (More)

Let k be a positive integer, and let G be a simple graph with vertex set V (G). A k-distance Roman dominating function on G is a labeling f : V (G) → {0, 1, 2} such that for every vertex with label 0, there is a vertex with label 2 at distance at most k from each other. The weight of a k-distance Roman dominating function f is the value ω(f) = v∈V f (v).… (More)

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