C++ Programme for total dominator chromatic number of ladder graphs through simple transformations

Abstract

A total dominator coloring of a graph \(\mathbb{G}=(\mathbb{V}, \mathbb{E})\) without isolated vertices, along with each vertex in \(\mathbb{G}\), is a proper coloring that dominates a color class. The total chromatic dominator number of \(\mathbb{G}\) is the minimum number of color classes with further assumption that each vertex in \(\mathbb{G}\) dominates a color class properly and is represented as \(\chi_{t d}(\mathbb{G})\). In this manuscript, we consider the chromatic total dominator number of ladder graphs through fundamental transformations via the program \(\mathrm{C}_{++}\).