2-Rainbow Domination Number of Some Graphs

Abstract

A 2-rainbow domination function of a graph G is a function f that assigns to each vertex a set ofcolors chosen from the set {1,2}, such that for any 𝑣 ∈ 𝑉(𝐺), 𝑓(𝑣) = ∅ implies ⋃𝑢∈𝑁(𝑣) |𝑓(𝑣)| ={1,2}. The 2-rainbow domination number 𝛾𝑟2(𝐺) of a graph G is minimum w(𝑓) = Σ𝑣∈𝑉(𝐺) |𝑓(𝑣)|over all such functions f. In this paper, we show that upper bounds of 2-rainbow dominationnumbers of several classes of graphs.