Volume 57, Number 2, March-April 2023
|Page(s)||383 - 399|
|Published online||15 March 2023|
Total dominator total chromatic numbers of cycles and paths
Department of Mathematics, University of Mohaghegh Ardabili, P.O. Box 5619911367, Ardabil, Iran
2 Department of Mathematics, Faculty of Basic Sciences, Ilam University, P.O. Box 69315-516, Ilam, Iran
* Corresponding author: email@example.com
Accepted: 15 October 2022
The total dominator total coloring of a graph is a total coloring of the graph such that each object (vertex or edge) of the graph is adjacent or incident to every object of some color class. The minimum number of the color classes of a total dominator total coloring of a graph is called the total dominator total chromatic number of the graph. In (A.P. Kazemi, F. Kazemnejad and S. Moradi, Contrib. Discrete Math. (2022).), the authors initiated to study the total dominator total coloring of a graph and found some useful results, and presented some problems. Finding the total dominator total chromatic numbers of cycles and paths were two of them which we consider them here.
Mathematics Subject Classification: 05C15 / 05C69
Key words: Total dominator total coloring / total dominator total chromatic number / total domination number / total mixed domination number / total graph
© The authors. Published by EDP Sciences, ROADEF, SMAI 2023
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