Total Dominator Total Chromatic Numbers of Wheels, Complete bipartite graphs and Complete graphs
Adel P. Kazemi, Farshad Kazemnejad
TL;DR
This paper investigates the total dominator total chromatic numbers for specific graph classes, including wheels, complete bipartite graphs, and complete graphs, by determining their minimal colorings.
Contribution
It introduces the concept of total dominator total coloring and computes the chromatic numbers for several fundamental graph types.
Findings
Total dominator total chromatic number of wheels is established.
Total dominator total chromatic number of complete bipartite graphs is determined.
Total dominator total chromatic number of complete graphs is calculated.
Abstract
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 wheels, complete bipartite graphs and complete graphs.
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph Labeling and Dimension Problems · graph theory and CDMA systems