منابع مشابه
Boundary powerful k-alliances in graphs
A global boundary defensive k-alliance in a graph G = (V,E) is a dominating set S of vertices of G with the property that every vertex in S has k more neighbors in S than it has outside of S. A global boundary offensive k-alliance in a graph G is a set S of vertices of G with the property that every vertex in V − S has k more neighbors in S than it has outside of S. We define a global boundary ...
متن کاملStrong Alliances in Graphs
For any simple connected graph $G=(V,E)$, a defensive alliance is a subset $S$ of $V$ satisfying the condition that every vertex $vin S$ has at most one more neighbour in $V-S$ than it has in $S$. The minimum cardinality of any defensive alliance in $G$ is called the alliance number of $G$, denoted $a(G)$. In this paper, we introduce a new type of alliance number called $k$-strong alliance numb...
متن کاملWeighted Alliances in Graphs
Let G = (V, E) be a graph and let W:V→N be a non-negative integer weighting of the vertices in V. A nonempty set of vertices S ⊆ V is called a weighted defensive alliance if ∀v ∈ S ,∑u∈N[v]∩S w(u) ≥ ∑x∈N(v)−S w(x). A non-empty set S ⊆ V is a weighted offensive alliance if ∀v ∈ δS ,∑u∈N(v)∩S w(u) ≥ ∑x∈N[v]−S w(x). A weighted alliance which is both defensive and offensive is called a weighted pow...
متن کاملSmall Alliances in Graphs
Let G = (V, E) be a graph. A nonempty subset S ⊆ V is a (strong defensive) alliance of G if every node in S has at least as many neighbors in S than in V \S. This work is motivated by the following observation: when G is a locally structured graph its nodes typically belong to small alliances. Despite the fact that finding the smallest alliance in a graph is NP-hard, we can at least compute in ...
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 Mathematics
سال: 2009
ISSN: 0012-365X
DOI: 10.1016/j.disc.2006.10.026