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- Dirk Meierling, Seyed Mahmoud Sheikholeslami, Lutz Volkmann
- Appl. Math. Lett.
- 2011

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)

Let G be a finite and simple graph with vertex set V (G), and let f : V (G) → {−1, 1} be a two-valued function. If k ≥ 1 is an integer and ∑x∈N(v) f(x) ≥ k for each v ∈ V (G), where N(v) is the neighborhood of v, then f is a signed total k-dominating function on G. A set {f1, f2, . . . , fd} of signed total k-dominating functions on G with the property that… (More)

- Odile Favaron, Hosein Karami, R. Khoeilar, Seyed Mahmoud Sheikholeslami
- Discrete Mathematics
- 2009

- Hosein Karami, R. Khoeilar, Seyed Mahmoud Sheikholeslami, Abdollah Khodkar
- Graphs and Combinatorics
- 2009

A set S of vertices of a graph G = (V, E)without isolated vertex is a total dominating set if every vertex of V (G) is adjacent to some vertex in S. The total domination number γt (G) is the minimum cardinality of a total dominating set of G. The total domination subdivision number sdγt (G) is the minimum number of edges that must be subdivided (each edge… (More)

- H. Aram, Seyed Mahmoud Sheikholeslami, Odile Favaron
- Discrete Mathematics
- 2009

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 sdγ (G) is the minimum number of edges that must be subdivided in order to increase the domination number. Velammal… (More)

- A. Bahremandpour, Fu-Tao Hu, Seyed Mahmoud Sheikholeslami, Jun-Ming Xu
- Discrete Math., Alg. and Appl.
- 2013

- Seyed Mahmoud Sheikholeslami, Lutz Volkmann
- Appl. Math. Lett.
- 2010

- Odile Favaron, Hosein Karami, Seyed Mahmoud Sheikholeslami
- Discrete Mathematics
- 2008

A paired-dominating set of a graph G = (V, E) with no isolated vertex is a dominating set of vertices inducing a graph with a perfect matching. The paired-domination number of G, denoted by γpr (G), is the minimum cardinality of a paired-dominating set of G. We consider graphs of order n ≥ 6, minimum degree δ such that G and G do not have an isolated vertex… (More)

- M. H. Akhbari, R. Hasni, Odile Favaron, Hosein Karami, Seyed Mahmoud Sheikholeslami
- Discrete Applied Mathematics
- 2010

A set S of vertices of a connected graph G is a doubly connected dominating set if every vertex not in S is adjacent to some vertex in S and the subgraphs induced by S and V − S are connected. The doubly connected domination number γcc(G) is theminimum size of such a set. We prove that when G and G are both connected of order n, γcc(G)+ γcc(G) ≤ n+ 3 and we… (More)

- J. Amjadi, N. Mohammadi, Seyed Mahmoud Sheikholeslami, Lutz Volkmann
- Discussiones Mathematicae Graph Theory
- 2014

Let D = (V,A) be a finite and simple digraph. A k-rainbow dominating function (kRDF) of a digraph D is a function f from the vertex set V to the set of all subsets of the set {1, 2, . . . , k} such that for any vertex v ∈ V with f(v) = ∅ the condition ⋃ u∈N(v) f(u) = {1, 2, . . . , k} is fulfilled, where N(v) is the set of in-neighbors of v. The weight of a… (More)