(Independent) $k$-Rainbow Domination of a Graph

Abstract

Let k be a positive integer and γ rk (G) (γ i rk (G)) be k-rainbow domination (independent k-rainbow domination) number of a graph G. In this paper, we study the k-rainbow domination and independent k-rainbow domination numbers of graphs. We obtain bounds for γ rk (G − e) (γ i rk (G − e)) in terms of γ rk (G) (γ i rk (G)). Finally, the relation between weak 3-domination and 3-rainbow domination number of graphs will be investigated.