Global Defensive Alliances in Graphs
نویسندگان
چکیده
منابع مشابه
On global (strong) defensive alliances in some product graphs
A defensive alliance in a graph is a set $S$ of vertices with the property that every vertex in $S$ has at most one moreneighbor outside of $S$ than it has inside of $S$. A defensive alliance $S$ is called global if it forms a dominating set. The global defensive alliance number of a graph $G$ is the minimum cardinality of a global defensive alliance in $G$. In this article we study the global ...
متن کاملGlobal 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 کاملGlobal defensive k-alliances in graphs
Let Γ = (V,E) be a simple graph. 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. A defensive k-alliance S is called global if it forms a dominating set. The global defensive k-alliance number of Γ, denoted by γ k(Γ), is the minimum cardinality of a defensive ...
متن کاملGlobal defensive alliances in star graphs
A defensive alliance in a graph G = (V,E) is a set of vertices S ⊆ V where for each v ∈ S, at least half of the vertices in the closed neighborhood of v are in S. A defensive alliance S is called global if every vertex in V (G) \S is adjacent to at least one member of the defensive alliance S. In this paper, we derive an upper bound to the size of the minimum global defensive alliances in star ...
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...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2003
ISSN: 1077-8926
DOI: 10.37236/1740