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A dominator coloring is a proper coloring of the vertices of a graph such that each vertex of the graph dominates all vertices of at least one color class (possibly its own class). The dominator chromatic number of a graph  G  is the minimum number of color classes in a dominator coloring of  G . In this paper, we determine the exact value of the dominator chromatic number of a subclass of forests which we call, generalized caterpillars forest, where every vertex of degree at least three is a support vertex.

On the dominator chromatic number of the generalized caterpillars forest