Total dominator coloring number of middle graphs
Farshad Kazemnejad, Behnaz Pahlavsay, Elisa Palezzato, Michele, Torielli
TL;DR
This paper investigates the total dominator coloring number of middle graphs, providing bounds for general graphs and trees, and calculating exact values for specific graph families.
Contribution
It introduces bounds for the total dominator chromatic number of middle graphs and computes exact values for several known graph families.
Findings
Bounds established for general graphs and trees.
Exact total dominator chromatic numbers computed for specific graph families.
Enhanced understanding of coloring properties of middle graphs.
Abstract
A total dominator coloring of a graph G is a proper coloring of G in which each vertex of the graph is adjacent to every vertex of some color class. The total dominator chromatic number of a graph is the minimum number of color classes in a total dominator coloring. In this article, we study the total dominator coloring on middle graphs by giving several bounds for the case of general graphs and trees. Moreover, we calculate explicitely the total dominator chromatic number of the middle graph of several known families of graphs.
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Taxonomy
TopicsGraph Labeling and Dimension Problems · Advanced Graph Theory Research