Aspects of upper defensive alliances
نویسندگان
چکیده
منابع مشابه
Global Defensive Alliances in Graphs
A defensive alliance in a graph G = (V,E) is a set of vertices S ⊆ V satisfying the condition that for every vertex v ∈ S, the number of neighbors v has in S plus one (counting v) is at least as large as the number of neighbors it has in V − S. Because of such an alliance, the vertices in S, agreeing to mutually support each other, have the strength of numbers to be able to defend themselves fr...
متن کاملDefensive k-alliances in graphs
Let Γ = (V,E) be a simple graph of order n and degree sequence δ1 ≥ δ2 ≥ · · · ≥ δn. For a nonempty set X ⊆ V , and a vertex v ∈ V , δX(v) denotes the number of neighbors v has in X. A nonempty set S ⊆ V is a defensive k-alliance in Γ = (V,E) if δS(v) ≥ δS̄(v) + k, ∀v ∈ S. The defensive k-alliance number of Γ, denoted by ak(Γ), is defined as the minimum cardinality of a defensive k-alliance in Γ...
متن کاملExact Defensive Alliances in Graphs
A nonempty set S ⊂ V is a defensive k-alliance in G = (V,E), k ∈ [−Δ,Δ] ∪ Z, if for every v ∈ S, dS(v) ≥ dS̄(v) + k. A defensive k-alliance S is called exact, if S is defensive k-alliance but is no defensive (k+1)-alliance in G. In this paper we study the mathematical properties of exact defensive k-alliances in graphs. In particular, we obtain several bounds for defensive k-alliance of a graph....
متن کاملOn defensive alliances and strong global offensive alliances
We consider complexity issues and upper bounds for defensive alliances and strong global offensive alliances in graphs. We prove that it is NP-complete to decide for a given 6-regular graph G and a given integer a, whether G contains a defensive alliance of order at most a. Furthermore, we prove that determining the strong global offensive alliance number γô(G) of a graph G is APX-hard for cubi...
متن کاملDefensive Alliances in Graphs of Bounded Treewidth
A set S of vertices of a graph is a defensive alliance if, for each element of S, the majority of its neighbors is in S. The problem of finding a defensive alliance of minimum size in a given graph is NP-hard and there are polynomial-time algorithms if certain parameters are bounded by a fixed constant. In particular, fixed-parameter tractability results have been obtained for some structural p...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2019
ISSN: 0166-218X
DOI: 10.1016/j.dam.2018.05.061