Total dominator chromatic number of graphs with specific construction

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 χ t d ( G ) of G is the minimum number of colors among all total dominator coloring of G . In this paper, we study the total dominator chromatic number of some graphs with specific construction. Also we compare χ t d ( G ) with χ t d ( G − eLet 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 χ t d ( G ) of G is the minimum number of colors among all total dominator coloring of G . In this paper, we study the total dominator chromatic number of some graphs with specific construction. Also we compare χ t d ( G ) with χ t d ( G − e ) , where e ∈ E ( G ) . ) , where e ∈ E ( G ) .