C++ Programme for total dominator chromatic number of cycles using elementary transformations

Abstract

A total dominator coloring of a graph \(G=(V, E)\) without isolated vertices is a proper coloring together with each vertex in \(G\) properly dominates a color class. The total dominator chromatic number of \(G\) is the minimum number of color classes with additional condition that each vertex in \(G\) properly dominates a color class and is denoted by \(\chi_{t d}(G)\). In this paper, we find the total dominator chromatic number of cycles using elementary transformations through \(\mathrm{C}_{+}+\) programme.