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on global (strong) defensive alliances in some product graphs
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نویسنده
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yero ismael gonzalez ,jakovac marko ,kuziak dorota
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منبع
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communications in combinatorics and optimization - 2017 - دوره : 2 - شماره : 1 - صفحه:21 -33
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چکیده
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A defensive alliance in a graph is a set s of vertices with the property that every vertex in s has at most one more neighbor 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.
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کلیدواژه
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defensive alliances ,global defensive alliances ,domination ,cartesian product graphs ,strong product graphs ,direct product graphs.
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آدرس
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universidad de cádiz, departamento de matematicas, spain, university of maribor, faculty of natural sciences and mathematics, slovenia, universidad de cadiz, departamento de estad´ıstica e investigaci´on operativa, spain
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پست الکترونیکی
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dorota.kuziak@urv.cat
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Authors
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