Total dominator total chromatic numbers of cycles and paths

TL;DR

This paper investigates the total dominator total chromatic number, a graph coloring concept, specifically determining this number for cycles and paths, which enhances understanding of graph coloring properties.

Contribution

It provides the first explicit calculations of the total dominator total chromatic numbers for cycles and paths, expanding the theory of graph colorings.

Findings

Total dominator total chromatic number for cycles is determined.

Total dominator total chromatic number for paths is established.

Results contribute to the broader understanding of graph coloring constraints.

Abstract

The total dominator total coloring of a graph is a total coloring of the graph such that each object of the graph is adjacent or incident to every object of some color class. The minimum namber of the color classes of a total dominator total coloring of a graph is called the total dominator total chromatic number of the graph. Here, we will find the total dominator chromatic numbers of cycles and paths.