Total dominator coloring of central graphs
Combinatorics
2018-05-09 v3
Abstract
A total dominator coloring of a graph is a proper coloring of 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 of it. Here, we study the total dominator coloring on central graphs by giving some tight bounds for the total dominator chromatic number of the central of a graph, join of two graphs and Nordhaus-Gaddum-like relations. Also we will calculate the total dominator chromatic number of the central of a path, a cycle, a wheel, a complete graph and a complete multipartite graph.
Cite
@article{arxiv.1801.05137,
title = {Total dominator coloring of central graphs},
author = {Farshad Kazemnejad and Adel P. Kazemi},
journal= {arXiv preprint arXiv:1801.05137},
year = {2018}
}