Rainbow Domination in Graphs
نویسندگان
چکیده
Assume we have a set of k colors and to each vertex of a graph G we assign an arbitrary subset of these colors. If we require that each vertex to which an empty set is assigned has in its neighborhood all k colors, then this is called the k-rainbow dominating function of a graph G. The corresponding invariant γrk(G), which is the minimum sum of numbers of assigned colors over all vertices of G, is called the k-rainbow domination number of G. In this paper we connect this new concept to usual domination in (products of) graphs, and present its application to paired-domination of Cartesian products of graphs. Finally, we present a linear algorithm for determining a minimum 2-rainbow dominating set of a tree.
منابع مشابه
Some Results on the Maximal 2-Rainbow Domination Number in Graphs
A 2-rainbow dominating function ( ) of a graph is a function from the vertex set to the set of all subsets of the set such that for any vertex with the condition is fulfilled, where is the open neighborhood of . A maximal 2-rainbow dominating function on a graph is a 2-rainbow dominating function such that the set is not a dominating set of . The weight of a maximal is the value . ...
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