Volume 55, 2021Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
|Page(s)||S1647 - S1655|
|Published online||02 March 2021|
On the dominator chromatic number of the generalized caterpillars forest
Laboratory of Mechanics, Physics and Mathematical Modeling, Faculty of Sciences, University of Médéa, Médéa, Algeria
2 LAMDA-RO Laboratory, Department of Mathematics, University of Blida, B.P. 270, Blida, Algeria
3 Department of Mathematics and Computer Science, Faculty of Sciences, University of Médéa, Médéa, Algeria
* Corresponding author: email@example.com
Accepted: 24 October 2020
A dominator coloring is a proper coloring of the vertices of a graph such that each vertex of the graph dominates all vertices of at least one color class (possibly its own class). The dominator chromatic number of a graph G is the minimum number of color classes in a dominator coloring of G. In this paper, we determine the exact value of the dominator chromatic number of a subclass of forests which we call, generalized caterpillars forest, where every vertex of degree at least three is a support vertex.
Mathematics Subject Classification: 05C15 / 05C69
Key words: Dominator coloring / dominator chromatic number / trees
© EDP Sciences, ROADEF, SMAI 2021
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