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.
Citation
Boštjan Brešar. Michael A. Henning. Douglas F. Rall. "RAINBOW DOMINATION IN GRAPHS." Taiwanese J. Math. 12 (1) 213 - 225, 2008. https://doi.org/10.11650/twjm/1500602498
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