BOUNDING THE RAINBOW DOMINATION NUMBER OF A TREE IN TERMS OF ITS ANNIHILATION NUMBER

A 2-rainbow dominating function (2rdf) of a graph g is a function f from the vertex setv (g) to the set of all subsets of the set f1; 2g such that for any vertex v 2 v (g) with f(v) = ; thecondition su2n(v) f(u) = f1; 2g is fulبهlled, where n(v) is the open neighborhood of v. the weight of a2rdf f is the value !(f) = pv2v jf(v)j. the 2-rainbow domination number of a graph g, denoted byr2(g), is the minimum weight of a 2rdf of g. the annihilation number a(g) is the largest integer ksuch that the sum of the rst k terms of the non-decreasing degree sequence of g is at most the numberof edges in g. in this paper, we prove that for any tree t with at least two vertices, r2(t)  a(t)+1.