Total dominator chromatic number of k-subdivision of graphs
Journal article
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Date
2023Metadata
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Original version
The Art of Discrete and Applied Mathematics. 2023, 6 (1), 10. 10.26493/2590-9770.1495.2a1Abstract
Let G be a simple graph. A total dominator coloring of G, is a proper coloring of the vertices of G in which each vertex of the graph is adjacent to every vertex of some color class. The total dominator chromatic (TDC) number χdt(G) of G, is the minimum number of colors among all total dominator coloring of G. For any k ∈ ℕ, the k-subdivision of G is a simple graph G1/k which is constructed by replacing each edge of G with a path of length k. In this paper, we study the total dominator chromatic number of k-subdivision of G.