منابع مشابه
Maximum Alliance-Free and Minimum Alliance-Cover Sets
A defensive k−alliance in a graph G = (V, E) is a set of vertices A ⊆ V such that for every vertex v ∈ A, the number of neighbors v has in A is at least k more than the number of neighbors it has in V −A (where k is the strength of defensive k−alliance). An offensive k−alliance is a set of vertices A ⊆ V such that for every vertex v ∈ ∂A, the number of neighbors v has in A is at least k more th...
متن کاملA Tight Bound on the Cardinalities of Maximum Alliance-Free and Minimum Alliance-Cover Sets
A defensive k-alliance in a graph G = (V, E) is a set of vertices A ⊆ V such that for every vertex v ∈ A, the number of neighbors v has in A is at least k more than the number of neighbors it has in V − A (k is a measure of the strength of alliance). In this paper, we deal with two types of sets associated with defensive k-alliances; maximum defensive k-alliance free and minimum defensive k-all...
متن کاملPartitioning a graph into alliance free sets
A strong defensive alliance in a graph G = (V, E) is a set of vertices A ⊆ V , for which every vertex v ∈ A has at least as many neighbors in A as in V − A. We call a partition A, B of vertices to be an alliance-free partition, if neither A nor B contains a strong defensive alliance as a subset. We prove that a connected graph G has an alliance-free partition exactly when G has a block that is ...
متن کاملAlliance free sets in Cartesian product graphs
Let G = (V,E) be a graph. For a non-empty subset of vertices S ⊆ V , and vertex v ∈ V , let δS(v) = |{u ∈ S : uv ∈ E}| denote the cardinality of the set of neighbors of v in S, and let S = V − S. Consider the following condition: δS(v) ≥ δS(v) + k, (1) which states that a vertex v has at least k more neighbors in S than it has in S. A set S ⊆ V that satisfies Condition (1) for every vertex v ∈ ...
متن کامل0 Fe b 20 06 Alliances versus cover and alliance free sets ∗
A defensive (offensive) k-alliance in Γ = (V,E) is a set S ⊆ V such that for every v ∈ S (v ∈ ∂S), the number of neighbors v has in S is at least k more than the number of neighbors it has in V \ S. A set X ⊆ V is defensive (offensive) k-alliance free, if for all defensive (offensive) k-alliance S, S \ X 6= ∅, i.e., X do not contain any defensive (offensive) k-alliance as a subset. A set Y ⊆ V ...
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ژورنال
عنوان ژورنال: Acta Mathematica Sinica, English Series
سال: 2011
ISSN: 1439-8516,1439-7617
DOI: 10.1007/s10114-011-0056-1