Total dominator chromatic number of Kneser graphs

Abstract

Decomposition into special substructures inheriting significant properties is an important method for the investigation of some mathematical structures. A total dominator coloring (briefly, a TDC) of a graph G is a proper coloring (i.e. a partition of the vertex set V(G) into independent subsets named color classes) in which each vertex of the graph is adjacent to all of vertices of some color class. The total dominator chromatic number (Formula presented.) of G is the minimum number of color classes in a TDC of G. In this paper among some other results and by using the existence of Steiner triple systems, we determine the total dominator chromatic number of the Kneser graph (Formula presented.) for each (Formula presented.).