Let G be a graph without isolated vertices. A total dominating set of G is a subset S of V(G) such that every vertex of G is adjacent to a vertex in S. The minimum cardinality of a total dominating set of G is denoted by gamma(t) (G). A 2-rainbow dominating function of G is a function f : V(G) -> 2({1,2}) such that for each nu E V(G) with f (nu) = empty set, boolean OR(u is an element of NG(nu)) f (u) = (1, 2). The minimum of Sigma (nu is an element of V(G)) vertical bar f(nu)vertical bar over all 2-rainbow dominating functions f of G is denoted by gamma(r2)(G).
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