Further results on maximal rainbow domination number

A 2-rainbow dominating function (2RDF) of a graph G is a function f from the vertex set V(G) to the set of all subsets of the set {1,2} such that for any vertex v∈V(G) with f(v)=∅ the condition ⋃u∈N(v)f(u)={1,2} is fulfilled, where N(v) is the open neighborhood of v. A maximal 2-rainbow dominating function of a graph G is a 2-rainbow dominating function f such that the set {w∈V(G)|f(w)=∅} is not a dominating set of G. The weight of a maximal 2RDF f is the value ω(f)=∑v∈V|f(v)|. The maximal 2-rainbow domination number of a graph G, denoted by γm2r(G), is the minimum weight of a maximal 2RDF of G. In this paper, we continue the study of maximal 2-rainbow domination {number} in graphs. Specially, we first characterize all graphs with large maximal 2-rainbow domination number. Finally, we determine the maximal 2-rainbow domination number in the sun and sunlet graphs.