Small alliances in a weighted graph
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 ...
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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...
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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...
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عنوان ژورنال:
- Discrete Applied Mathematics
دوره 158 شماره
صفحات -
تاریخ انتشار 2010