(k, r)-Domination in Graphs
نویسندگان
چکیده
Let G = (V,E) be a simple graph. A subset Dof V (G) is a (k, r)dominating set if for every vertexv ∈ V −D, there exists at least k vertices in D which are at a distance utmost r from v in [1]. The minimum cardinality of a (k, r)-dominating set of G is called the (k, r)-domination number of G and is denoted by γ(k,r)(G). In this paper, minimal (k, r)dominating sets are characterized. It is proved that Vizing conjecture does not hold in the case of (k, r)-domination. Mathematics Subject Classification: 05C69
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