Computing global offensive alliances in Cartesian product graphs
نویسندگان
چکیده
منابع مشابه
Computing global offensive alliances in Cartesian product graphs
A global offensive alliance in a graph G is a set S of vertices with the property that every vertex not belonging to S has at least one more neighbor in S than it has outside of S. The global offensive alliance number of G, γo(G), is the minimum cardinality of a global offensive alliance in G. A set S of vertices of a graph G is a dominating set for G if every vertex not belonging to S has at l...
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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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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 کاملOffensive alliances in graphs
A set S is an offensive alliance if for every vertex v in its boundary N(S)−S it holds that the majority of vertices in v’s closed neighbourhood are in S. The offensive alliance number is the minimum cardinality of an offensive alliance. In this paper we explore the bounds on the offensive alliance and the strong offensive alliance numbers (where a strict majority is required). In particular, w...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2013
ISSN: 0166-218X
DOI: 10.1016/j.dam.2012.08.009