Global offensive k-alliance in bipartite graphs
نویسندگان
چکیده
منابع مشابه
GLOBAL OFFENSIVE k-ALLIANCE IN BIPARTITE GRAPHS
Let k ≥ 0 be an integer. A set S of vertices of a graph G = (V (G), E(G)) is called a global offensive k-alliance if |N(v) ∩ S| ≥ |N(v) − S| + k for every v ∈ V (G) − S, where 0 ≤ k ≤ ∆ and ∆ is the maximum degree of G. The global offensive k-alliance number γ o (G) is the minimum cardinality of a global offensive k-alliance in G. We show that for every bipartite graph G and every integer k ≥ 2...
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Let G = (V (G), E(G)) be a graph, and let k ≥ 1 be an integer. A set S ⊆ V (G) is called a global offensive k-alliance if |N(v) ∩ S| ≥ |N(v)−S|+k for every v ∈ V (G)−S, where N(v) is the neighborhood of v. The global offensive k-alliance number γ o (G) is the minimum cardinality of a global offensive k-alliance in G. We present different bounds on γ o (G) in terms of order, maximum degree, inde...
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Let G be a simple graph with vertex set V (G). A non-empty set S ⊆ V (G) is a global strong offensive alliance if for every vertex v in V (G)−S, a strict majority of its closed neighborhood is in S. The global strong offensive alliance number γô(G) is the minimum cardinality of a global strong offensive alliance of G. We show that if G is a connected bipartite graph of order at least three, the...
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We consider finite graphs G with vertex set V (G). For a subset S ⊆ V (G), we define by G[S] the subgraph induced by S. By n(G) = |V (G)| and δ(G) we denote the order and the minimum degree of G, respectively. Let k be a positive integer. A subset S ⊆ V (G) is a connected global offensive k-alliance of the connected graphG, ifG[S] is connected and |N(v)∩S| ≥ |N(v)−S|+k for every vertex v ∈ V (G...
متن کاملOn global offensive k-alliances in graphs
We investigate the relationship between global offensive k-alliances and some characteristic sets of a graph including r-dependent sets, τ dominating sets and standard dominating sets. In addition, we discuss the close relationship that exist among the (global) offensive ki-alliance number of Γi, i ∈ {1, 2} and the (global) offensive k-alliance number of Γ1×Γ2, for some specific values of k. As...
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ژورنال
عنوان ژورنال: Opuscula Mathematica
سال: 2012
ISSN: 1232-9274
DOI: 10.7494/opmath.2012.32.1.83