Total dominator chromatic number of a graph

Given a graph $G$, the total dominator coloring problem seeks a proper coloring of $G$ with the additional property that every vertex in the graph is adjacent to all vertices of a color class. We seek to minimize the number of color classes. We initiate to study this problem on several classes of gr...

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Bibliographic Details
Published in:Transactions on combinatorics 2015-06, Vol.4 (2), p.57-68
Main Author: Adel P. Kazemi
Format: Article
Language:English
Subjects:
chromatic number
total domination number
Total dominator chromatic number
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Summary:Given a graph $G$, the total dominator coloring problem seeks a proper coloring of $G$ with the additional property that every vertex in the graph is adjacent to all vertices of a color class. We seek to minimize the number of color classes. We initiate to study this problem on several classes of graphs, as well as finding general bounds and characterizations. We also compare the total dominator chromatic number of a graph with the chromatic number and the total domination number of it.
ISSN:2251-8657
2251-8665