0 Fe b 20 06 Alliances versus cover and alliance free sets ∗
نویسنده
چکیده
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 is a defensive (offensive) k-alliance cover, if for all defensive (offensive) k-alliance S, S ∩ Y 6= ∅, i.e., Y contains at least one vertex from each defensive (offensive) k-alliance of Γ. In this paper we obtain several mathematical properties of defensive (offensive) k-alliances, k-alliance free sets and k-alliance cover sets, and we explore some of their interrelations.
منابع مشابه
Strong Alliances in Graphs
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