Some bounds on global alliances in trees
نویسندگان
چکیده
منابع مشابه
Some Bounds on Alliances in Trees
Given a simple graph G = (V,E), a subset S of the vertices is called a global defensive alliance if S is a dominating set and for every vertex v in S at least half of the vertices in the closed neighborhood of v are in S. Similarly, a subset S is called a global offensive alliance if S is a dominating set and for every vertex v not in S at least half of the vertices in the closed neighborhood o...
متن کاملOn 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 Alliances and Independence in Trees
A global defensive (respectively, offensive) alliance in a graph G = (V,E) is a set of vertices S ⊆ V with the properties that every vertex in V − S has at least one neighbor in S, and for each vertex v in S (respectively, in V − S) at least half the vertices from the closed neighborhood of v are in S. These alliances are called strong if a strict majority of vertices from the closed neighborho...
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Let p be a positive integer andG= (V ,E) a graph. A subset S of V is a p-dominating set if every vertex of V − S is dominated at least p times, and S is a p-dependent set of G if the subgraph induced by the vertices of S has maximum degree at most p − 1. The minimum cardinality of a p-dominating set a ofG is the p-domination number p(G) and the maximum cardinality of a p-dependent set ofG is th...
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A dominating set S of a graph G is a global (strong) defensive alliance if for every vertex v ∈ S, the number of neighbors v has in S plus one is at least (greater than) the number of neighbors it has in V \ S. The dominating set S is a global (strong) offensive alliance if for every vertex v ∈ V \ S, the number of neighbors v has in S is at least (greater than) the number of neighbors it has i...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2013
ISSN: 0166-218X
DOI: 10.1016/j.dam.2011.11.026