2018/01/19 by Saeid Alikhani, Saeid Alikhani, Alikhani, Saeid +4 · 1 citation
Computer Science · Mathematics · #Advanced Graph Theory Research #Graph Labeling and Dimension Problems #Limits and Structures in Graph Theory #math.CO #msc:05C15 #msc:05C69
paper · pdf · doi:10.48550/arxiv.1801.06500
11 pages, 5 figures
arxiv created 2018/01/19 · arxiv updated 2018/01/22
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 G(1)/(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.