دوستعلی مژده

Let G=(V(G),E(G)) be a graph. A function f:V(G)→𝒫{1,2} is a 2-rainbow dominating function if for every vertex x with f(x)=𝜙, f(N(x))= {1,2}, where 𝒫 {1,2} is the power set of {1,2}. The 2-rainbow domination number 𝛾r2 (G) is the minimum weight of ∑_(v ∊V(G))|f(v)| taken over all 2-rainbow dominating functions f. An outer-independent 2-rainbow dominating function (OI2-rD function) of G is a 2-rainbow dominating function f such that the set of all v∊V(G) with f(v)=𝜙 is independent. The outer independent 2-rainbow domination number (OI2-rD number) 𝛾oir2(G) is the minimum weight of an OI2-rD function of G. In this paper, we study the OI2-rD number of graphs. Moreover, we characterize graphs with 𝛾 oir2(G) ∊{2,n}.