Total dominator chromatic number of Mycieleskian graphs
Abstract
A total dominator coloring of a graph G is a proper coloring of G in which each vertex of the graph is adjacent to every vertex of some color class. The total dominator chromatic number Xd{G) °f G is the minimum number of color classes in a total dominator coloring of it. In [Total dominator chromatic number of a graph, Transactions on Combinatorics, Vol. 4 No. 2 (2015) 57-68] the author initialed to study this parameter in graphs and obtained some important results. Here, we continue it in Mycieleskian graphs. We show that the total dominator chromatic number of the Mycieleskian of a graph G is Xd(G) + l or Xd(G) + 2> and then characterize graphs G that the total dominator chromatic number of M(G) is Xd(G) + 1 or Xdt(G) + 2. © 2015 Utilitas Mathematics.
