On global (strong) defensive alliances in some product graphs
نویسندگان
چکیده مقاله:
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 defensive alliances in Cartesian product graphs, strong product graphs and direct product graphs. Specifically we give several bounds for the global defensive alliance number of these graph products and express them in terms of the global defensive alliance numbers of the factor graphs.
منابع مشابه
Global Defensive Alliances in Graphs
A defensive alliance in a graph G = (V,E) is a set of vertices S ⊆ V satisfying the condition that for every vertex v ∈ S, the number of neighbors v has in S plus one (counting v) is at least as large as the number of neighbors it has in V − S. Because of such an alliance, the vertices in S, agreeing to mutually support each other, have the strength of numbers to be able to defend themselves fr...
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عنوان ژورنال
دوره 2 شماره 1
صفحات 21- 33
تاریخ انتشار 2017-06-01
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