Global Alliance Partition in Trees
نویسندگان
چکیده
Let G be a connected graph with vertex set V (G) and edge set E(G). A (defensive) alliance in G is a subset S of V (G) such that for every vertex v ∈ S, |N [v]∩S| ≥ |N(v)∩(V (G)− S)|. The alliance partition number, ψa(G), was defined (and further studied in [11]) to be the maximum number of sets in a partition of V (G) such that each set is a (defensive) alliance. Similarly, ψg(G) is the maximum number of sets in a partition of V (G) such that each set is a global alliance, i.e. each set is an alliance and a dominating set. In this paper, we give bounds for the global alliance partition number in terms of the minimum degree, which gives exactly two values for ψg(G) in trees. We concentrate on conditions that classify trees to have ψg(G) = i (i = 1, 2), presenting a characterization for binary trees.
منابع مشابه
Alliance Partition Number in Graphs
Let G be a graph with vertex set V (G) and edge set E(G). A defensive alliance in G is a subset S of V (G) such that for every vertex v ∈ S, |N [v] ∩ S| ≥ |(V (G)−N [v]) ∩ S|. A global defensive alliance is an alliance that is also a dominating set. We define the alliance partition number, ψa(G) (global alliance partition number, ψg(G)), to be the maximum number of sets in a partition of V (G) ...
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