Seyed Mahmoud Sheikholeslami

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For a positive integer k, a k-rainbow dominating function of a graph G is a function f from the vertex set V (G) to the set of all subsets of the set {1, 2,. .. , k} such that for any vertex v ∈ V (G) with f (v) = ∅ the condition u∈N (v) f (u) = {1, 2,. .. , k} is fulfilled, where N (v) is the neighborhood of v. The 1-rainbow domination is the same as the(More)
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 (each edge in G can be subdivided at most once) in order to(More)
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)
Let G be a simple graph without isolated vertices with ver-tex set V (G) and edge set E(G) and let k be a positive integer. A function f : E(G) → {−1, 1} is said to be a signed star k-dominating function on G if e∈E(v) f (e) ≥ k for every vertex v of G, where E(v) = {uv ∈ E(G) | u ∈ N (v)}. A set {f1, f2,. .. , f d } of signed star k-dominating functions on(More)