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

Authors : Zhila MANSOURİ, Doost Ali MOJDEH

Pages : 128-135

Doi:10.47000/tjmcs.691030

View : 45 | Download : 11

Publication Date : 2020-12-31

Article Type : Research Paper

Abstract :Let $G=insert ignore into journalissuearticles values(V,E);$ be a graph with the vertex set $V=Vinsert ignore into journalissuearticles values(G);$ and the edge set $E=Einsert ignore into journalissuearticles values(G);$. Let $k$ be a positive integer and $\gamma_{rk}insert ignore into journalissuearticles values(G);$ insert ignore into journalissuearticles values($\gamma_{i_{rk}}insert ignore into journalissuearticles values(G);$); be $k$-rainbow domination insert ignore into journalissuearticles values(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 $\gamma_{rk}insert ignore into journalissuearticles values(G-e);$ insert ignore into journalissuearticles values($\gamma_{i_{rk}}insert ignore into journalissuearticles values(G-e);$); in terms of $\gamma_{rk}insert ignore into journalissuearticles values(G);$ insert ignore into journalissuearticles values($\gamma_{i_{rk}}insert ignore into journalissuearticles values(G);$);. Finally, the relation between weak $3$-domination and $3$-rainbow domination number of graphs will be investigated.
Keywords : Rainbow domination, independent rainbow domination, graphs

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