‎Dominator coloring of a graph is a proper (vertex) coloring with the property that every vertex is either alone in its color class or adjacent to all vertices of at least one color class‎. ‎A dominated coloring of a graph is a proper coloring such that every color class is dominated with at least one vertex‎. ‎The dominator chromatic number of corona products and of edge corona products is determined‎. ‎Sharp lower and upper bounds are given for the dominated chromatic number of edge corona products‎. ‎The dominator chromatic number of hierarchical products is bounded from above and the dominated chromatic number of hierarchical products with two factors determined‎. ‎An application of dominated colorings in genetic networks is also proposed‎.

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