Closed formulas for 2-domination and 2-outer-independent domination numbers of rooted product graphs

set of vertices W⊆ V(G) of a graph G with no isolated vertex is said to be a 2-dominating set of G if every vertex in V(G)∖ W is adjacent to at least two vertices in W . In addition, if V(G)∖ W is an independent set, then W is said to be a 2-outer-independent dominating set of G . The 2-domination number (2-outer-independent domination number) of G is the minimum cardinality among all 2-dominating sets (2-outer-independent dominating sets) of G . In this paper we study the above two parameters for the case of the rooted product graphs. In particular, we obtain closed formulas (three possible expressions) for each of these domination parameters, and we also characterise the graphs that satisfy each of these formulas. As a consequence of the study, we obtain the corresponding formulas for the corona product graphs.