Alliance Partition Number in Graphs
نویسندگان
چکیده
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) such that each set is a defensive alliance (gloabal defensive alliance). In this paper, we give both general bounds and exact results for the alliance partition number and for the global alliance partition number, as well as connection between the two.
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ورودعنوان ژورنال:
- Ars Comb.
دوره 103 شماره
صفحات -
تاریخ انتشار 2012