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- W1557513888 abstract "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 $gamma_{{rm r}k}(G)$, 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." @default.
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- W1557513888 date "2008-02-01" @default.
- W1557513888 modified "2023-09-26" @default.
- W1557513888 title "RAINBOW DOMINATION IN GRAPHS" @default.
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- W1557513888 doi "https://doi.org/10.11650/twjm/1500602498" @default.
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