Study on Total Dominator Colorings in Paths

Abstract

In this paper we determine total dominator chromatic number in paths. Let  be a graph without isolated vertices. A total dominator coloring of a graph G is a valid colouring of the graph G with the additional feature that each vertex in the graph G dominates a color class properly. The total dominator chromatic number of G is the fewest number of colors for which there is a total dominator coloring of G, and it is indicated by . The total dominator chromatic number in paths is determined in this research. n denotes an integer greater than or equal to 2 unless otherwise specified.