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arXiv · 1801.05137

Total dominator coloring of central graphs

Farshad Kazemnejad·Adel P. Kazemi
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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 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.

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Farshad Kazemnejad, Adel P. Kazemi. 2018-01-16. Total dominator coloring of central graphs. https://arxiv.org/abs/1801.05137

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