  For a simple graph $G$, a domination coloring of $G$ is a proper vertex
coloring such that every vertex of $G$ dominates at least one color class, and
every color class is dominated by at least one vertex. The domination chromatic
number, denoted by $\chi_{dd}(G)$, is minimum number of colors among all
domination colorings of $G$. In this paper, we discuss the effects of some
typical operations on $\chi_{dd}(G)$, such as vertex (edge) removal, vertex
(edge) contraction, edge subdivision, and cycle extending.
