Total dominator chromatic number of some operations on a graph

Let G be a simple graph. A total dominator coloring of G is a proper coloring of the vertices of G in which each vertex of the graph is adjacent to every vertex of some color class. The total dominator chromatic number Xtd(G) of G is the minimum number of colors among all total dominator coloring of G. In this paper, we examine the effects on Xtd(G) when G is modified by operations on vertex and edge of G.