Domination related parameters in rooted product graphs
  A set $S$ of vertices of a graph $G$ is a dominating set in $G$ if every vertex outside of $S$ is adjacent to at least one vertex belonging to $S$. A domination parameter of $G$ is related to those sets of vertices of a graph satisfying some domination property together with other conditions on the vertices of $G$. Here, we investigate several domination related parameters in rooted product graphs. 
Dorota Kuziak, Magdalena Lemanska and Ismael G. Yero
math.CO